Backdooring typically refers to the act of taking out an enemies base tower or inhibitor/barracks while the enemy team is slow to respond to your presence, unaware of your advances on their base (due to poor map vision coverage), or otherwise occupied with fighting or pushing on their own.
Generally speaking, in League of Legends, a backdoor will occur while one team is pushing on 5v4, while the last remaining member of the defending team goes to take out towers. Strong backdoor champions include Master Yi (due to his high autoattack damage, steroid skills, and high mobility), Twisted Fate (long range ultimate), Pantheon (long range ultimate), or any other character that excels in dealing auto-attack damage and pushing.
Backdooring is not explicitly disallowed, nor is it a core part of gameplay (meaning you wont see a backdoor happen every game). However, as a rule of thumb, it's generally looked down upon by people in mid to low ELO brackets. You generally wont see it happen as much in higher level play as the enemy will be much more attentive of problem characters like that and wont give them the chance to do so. It's a perfectly legitimate tactic, just difficult to pull off in higher levels of play.
It should be noted that you should not be confusing "backdooring" with "split pushing". Split pushing is when the offensive team attempts to take down two or more towers simultaneously through the use of a single lane distraction. For example, a team may send 3 players to a single lane to push on the tower. The defending team overcompensates and sends all 5 to defend said tower and hopefully secure a few kills. Meanwhile, the other 2 offensive players have full potential to go and destroy another lane's tower.
In both cases, you can utilize long range ultimate characters like Pantheon, Twisted Fate, Nocturne, Shen or Karthus to dissuade or completely stop split pushing / backdooring. Additionally, the summoner spells Teleport and Fortify are great for preventing these tactics. It's not uncommon to have at least one person running Teleport on a team, and in Draft matches (where you have the ability to see the enemy team during champion select), it's often wise to have one character take Fortify if you identify their team as a push team.
There's not really a "genre label" for this kind of gaming, simply because non-interactive games aren't much of a game genre. Most of the ones that exist are either silly idling games (Idle RPG/Progress Quest/Idle 2), bots (like this one that plays a roguelike by itself), or more AI experiment than game (Conway's Game of Life, for instance).
I think that "Zero Player Games" or "bot game" is about the best you can do. I did find some interesting articles when I searched for "games that play themselves."
There's also a subgenre of the strategy genre where you'll find games where you can only interact indirectly with the game world, with games like Populous or Evil Genius. This subgenre is generally called "Artificial Life" or "God Game".
Some games are capable of playing themselves, in a demo or "attract" mode. Arcade games are especially fond of this, as it attracts people to the cabinet and shows them what they might get for dropping in a quarter.
If we consider things like ProgressQuest games, then screensavers might be considered non-interactive games as well (or in reverse, non-interactive games might be screensavers). There was one screensaver for Win95 that played a little maze, for instance. Of course, there's also the iconic After Dark package that not only featured a number of things you might consider to be non-interactive games, but also some screensavers that were fully playable, like Lunatic Fringe.
Part of the problem is that we already have many non-interactive forms of digital entertainment. We give them many terms, but one is "movie." You could consider a movie like Scott Pilgrim vs. The World to be a "game that plays itself." The protagonist even levels up, has extra lives, and fights a final boss. Or, take the movie Clue, which went so far as to include multiple endings, and each time you went to see it there was a chance you'd see a different one. (I realize that's tangential, but it's sort of an interesting aside to your question.)
"Non Games" is a similar term, but it's more for games that have no goal, like Mario Paint. These games ride the line between game and application.
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I guess you're speaking about cel shading as @pinckerman said in the comments. More information right here.
By the way, Zelda the Wind Waker was already in that style.