This would really depend on the game! If it was any old game that happened to be on TV, and you couldn't be bothered to study so were easily distracted, it would be 'a' game. If it was a really important game you planned to watch even though you should have been studying, it would be 'the' game.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.