I can't speak to chess, but it is the word for "stones are about to be captured" in the game of go. Its the English word for this as well (most go terms in English are taken from Japanese).

As gizmo686 has said, it's from go, and it isn't really that similar to check in chess. In shogi (the traditional Japanese equivalent to chess) the word for check is "ōte" (literally "king move").

The misconception is because sometimes beginners are introduced to the term by relating it the way the player says "check" in chess when a configuration of pieces would result in danger for the king. It's a similar idea but in go the stakes of Atari is a lot lower (lose 1 stone instead of the whole game).

A lot more than one stone can be (and often is) at risk in an atari, and an atari situation can absolutely determine the winner of a game.

Sorry, I posted the same before seeing your response.