[RPG] One player likes faster-paced games, but the rest enjoy smelling the roses

You're not having fun.

Since the entire point of role-playing is to have fun, you need to do something about it. In particular, it sounds like the character he's playing (called a GMPC) is seriously distracting him from his GM task of running a fun story for the other players at the table.

You have several options, depending on whether you're willing to accept him as a GM as long as he changes, or if you can accept him as a part of the group as long as he isn't GMing:

1. Talk to the GM about his behavior. Try to be non-confrontational, and don't have this conversation in front of the group; that will just make him defensive and won't accomplish anything. Try persuading him to not bring a character along with the group; he's GMing, not playing.
2. Sit out the current game, until the GM is done. There's no need for you to continue playing a game you dislike, so take a break until he's done running the game. Then join the next game, that someone else in the group will run.
3. Take over GMing duties, with the support of the rest of the group. Since they already asked you to be the GM, they'll almost certainly be willing to let you run the game. Talk to the other players about this individually before you try this; if you have enough support, you'll be able to usurp his position as GM, and start an entirely different game. Perhaps the current GM will be a better player than they are a GM. And look on the bright side: you now have some fantastic examples of how not to GM, which will make you much better at this new role! You can also combine this with #2 above: sit out the game until it's over, then be the next GM. (Warning: given what you've described of his personality, the current GM is unlikely to take this well.)
4. Start a separate gaming group, inviting whoever is willing to play without the problem GM. If some people are unwilling to play with the new group because they don't want to exclude the current GM, then you'll need to exclude them as well. Recruit a few other players from elsewhere if you need to.
5. Find a new gaming group. If all else fails, just don't play with this group at all. If they're willing to play with someone they dislike, and you can't persuade them to kick out a problem GM, that's their problem. It doesn't have to be your problem.

Note that none of these options include playing a game you dislike with a GM who you hate. He isn't going to improve on his own, unless you talk him into changing or encourage the group to leave him behind.

On a slight tangent, see the Geek Social Fallacies. It sounds like some of the members of the gaming group are suffering from GSF #1: "Don't exclude anyone" and GSF #5: "Failing to invite someone is a deliberate snub."

Disclaimer

1. Your ability to constructively address things like this as a player will, perhaps unfortunately, depend on how central or peripheral you are to the group socially. And this is definitely a social problem, not just a game problem, so I'll be attempting to channel Captain Awkward for much of this answer. But I wanted to start out by admitting the possibility that you may not have "standing" to address this issue other than bringing it to the GM's attention, which it sounds like you've already done. I hate to say it, but this may be especially true depending on the nature of your relationship with the GM; some people will make assumptions that could make it more difficult for you to bring up issues, unjust though that may be.
   • Note that I don't think that means you shouldn't say something. The GM's role in "running the game" depends on the system and the particular game, but that need not and often should not translate to running the gaming group. Some situations are customarily addressed by the GM as an extension of their role as referee, but in real life the GM isn't in charge of anyone else, and it's unfair to always expect them to solve table problems - mayking the game fun is everyone's responsibility.
2. Most of the below is written based on the assumption that the problem player here is basically operating in good faith, but frustrated with how things are going and expressing it badly. This may not be true - frankly, dude sounds like a pain, and you could choose to be more assertive - but there are reasons to at least verbally leave open the possibility:
   • Having been the guy who was doing something wrong and didn't find out until later, I really appreciate being given the benefit of the doubt.
   • It can make for smoother, less confrontational conversations.
   • It's kinder to give people some credit/dignity, even if they don't deserve it, which is more important the more invested you and others are in maintaining the relationship.
   • It will often make it pretty obvious if they are operating in bad faith and don't care about your feelings, which is disappointing but makes it easier to do what you have to do next.

The Simple Way

Don't play with him. You're there to have fun, and he's making things not fun. If your comment about what he wants is accurate, and that would indeed ruin the game for the rest of you, then there's probably no way for everyone to get what they want, so majority rules. Of course, this is simple in concept but not necessarily in execution; still, it's preferable to letting resentment build into an explosion that leads to the same result but with even more hurt feelings.

Now, normally this would be done by the GM, in a private conversation, but if they agree it needs to happen but don't want to do it themselves for social reasons, it could be easier if done as a group, and you could start that conversation. Probably after or towards the end of a session, when he's been up to his usual shenanigans, I would call him on it and say "Hey, it really makes it less fun when you do X, and you don't really seem to be enjoying the game that much yourself. Since we seem to have such different styles, is it possible this specific game, with these rules and expectations, isn't really your thing?"

Note that this doesn't have to be personal, though it's difficult not to take something like this personally, partly due to Geek Social Fallacy #5: the idea that friends do everything together and therefore not wanting do do a particular activity together must mean you're not friends. To mitigate that, you could suggest specific, reassuring alternatives: "I don't think this game is working out as is, but maybe you and I could do [ACTIVITY] on [WEEKDAY] instead?" Don't suggest that if you wouldn't actually enjoy it, but perhaps you could arrange for someone who would to do so.

The Complex Way

Try to resolve the situation in a way that lets you keep playing this or a similar game. Ask this player to help you understand what makes them act this way - why they do the things they do, and why they respond the way they do to your actions (because the examples you gave really, really don't sound like any definition of metagaming i'm familiar with). This will be a long, possibly multi-part conversation. Two broad categories of possibilities, likely both present in some proportion:

1. Something is going on in their personal life that makes them easily frustrated when things don't go their way; either a generic stressor or tension in their relationship with another player(s). You likely can't solve the root problem at the table, but pointing it out could help them realize they need to keep it out of the game.
2. They want to play the game one way, you all want to play it a different way, and most likely, this gap was not identified, discussed, and resolved before play began. Different players are motivated by wildly different things. It may be possible to craft a game that meets everyone's needs at least some of the time - a little character drama here, a little violently eviscerating anyone who stands in your way over there. This is mostly on the GM, but also about character design - sometimes having the more fight-y players play more fight-y characters, like bodyguards, can ease the tension. They're still not talking much and still more interested in killing, but now it's in character. Heck, sometimes just the act of pointing out that there are multiple equally valid ways of playing games by itself can help, if part of the frustration comes from a feeling that the other players are doing something objectively Wrong as opposed to "not what we're going for this time."

If you can't find common ground after working on it for a while, you still have The Simple Way, and at least you know you tried.

Either Way

1. Focus on a specific, recent incident or two. You can allude to the fact that it's becoming kind of a pattern, but "You always..." is not the start of a productive conversation. Presumably, this player hasn't been thinking about this issue as much as you have, so a narrow, concrete focus will help them have information to work with.

2. Use I-statements. Saying "You need to stop doing X", while very possibly true, can sound too much like "Your behavior is bad and wrong and so are you."¹ Saying "I really thought I was playing my character, and I wasn't out to get you, so I was hurt when you accused me of that," highlights the effect their actions are having and invites them to reconsider.

3. Avoid an "intervention" vibe. Especially since you're not the GM, try not to speak for anyone else; just mention your issues with this player's behavior. There may come a point in the conversation where it's appropriate to invite others to share their opinions, but anything like "We've decided..." sounds too much like "We've all been talking about you behind your back, and the conclusion is that you suck!"

_{¹This point applies in cases of mildly annoying behavior where you're trying to keep things friendly. When the stakes are higher, like if the behavior is making people feel unsafe, it's much more important to be clear about "You need to stop doing this, now." I'm interpreting this situation as the former, but I could be wrong and either way I wouldn't want people to generalize too much from this point of the answer.}