Here is a tic-tac-toe version https://en.wikipedia.org/wiki/Tic-tac-toe_variants

And a chess version https://en.wikipedia.org/wiki/Losing_Chess

A large (finite?) list of chess variants also exists https://en.wikipedia.org/wiki/List_of_chess_variants

To be expected but nonetheless amazing how changing one bit in the game rules can have strong effects in gameplay and strategy.