Another big difference is turn-based vs real-time games. Although both players in a chess game use a timer, making a move a tenth of a second later usually won’t make a significant change on the outcome. This is not the case for real-time games like FPSs, where a bot that can react faster than any human can will always win.
It’s an apples to oranges comparison. FPS bots are not playing the same game: they have perfect information in an imperfect information game.
Another big difference is turn-based vs real-time games. Although both players in a chess game use a timer, making a move a tenth of a second later usually won’t make a significant change on the outcome. This is not the case for real-time games like FPSs, where a bot that can react faster than any human can will always win.