Yes 99.9% it would mean the best possible game. It can also mean a game about games in the very rare case that someone wants to say something like that though, like the use of the meta- prefix in English.
"Αγώνας" can also mean "struggle" or "fight" (e.g. ο αγώνας για την ελευθερία = the fight/stuggle for freedom), but not "battle". Also, this is a lesson on sports and the world "αγώνας" in this context would mean game/match.