Learn English – How had you known

Since when do you know each other?

connotes doubt or even incredulity that the two people in question know each other at all. "Since when" is synonymous with "How long has this been true without my knowing it?" The asker of the question is less interested in finding out the length of time than in communicating their surprise.

Since when have you known each other?

asks when the two people in questions first met. It would normally (but not necessarily) be answered with a specific moment, e.g. "Since 2013" or "Since yesterday"

Another alternative is:

How long have you known each other?

This would normally be answered with a duration of time, e.g. "For three years", or "For a couple of days".

If someone asked me, "how long have you played this game?", I would take it to be asking about the amount of time since I started playing - i.e. if I started playing a year ago, I would reply, "about a year".

I would say the same thing if someone asked me, "how long have you been playing this game?" The verb tenses "played" and "been playing" are different -- but "been playing" means that the playing is still going on, which is definitely the case if you're asking inside the game.

For example, I played Quake 3 for 2 years. Since I'm no longer playing Quake 3, "how long have you been playing" isn't appropriate - "played" is the better verb tense because the action concluded in the past.

None of this has any bearing on the current round. In my opinion, the better way to ask that question is to change the noun, not change the verb tense. For example:

How long has this round been going on?

^^ This means that the round is still ongoing.

How long was that round?

^^ This means the round has ended.