This entry refers to a type of abstract game and not to games where participants try to reach an end condition as fast as possible. For that, check the Race page.
A Race Game is the collective term for non-one-player games where there is a low (or even no) amount of interactivity between the players.
We can extrapolate from this defintion that in race games the win condition must not be influenced by the actions of any of the other players, and if it is, it must be in very minor amounts. In practice, this results in the fact that while all players are technically playing the same game, in practice they’re all playing a singleplayer game with other people sitting around them, and eventually everyone stops to compare results.
An obvious example of this type of game would be a footrace, where interacting with other players would disqualify you. Note however that vehicle racing games would likely not count, as you do and are often encouraged to interact with the other players via items or just slamming into them.