According to basic grammar, there should be a be verb in front of the Over. So why do all games display Game Over instead of Game Is Over?
It's idiomatic short for
Games used to have to deal with very limited resources like screen space, and it made sense to try and keep messages short and clear, also to avoid burdening the player with having to read a lot of text. (Imagine "Dear player, we are sorry to inform you that notwithstanding your great efforts, your gaming experience has now been terminated".)
Games have copied the use of common signs in that: they are quickly recognizable, even though they may not contain a full grammatical sentence. "Exit" successfully conveys the meaning of "this way you will find a way to leave the premises", "Ladies" in the same manner makes clear the presence of sanitary facilities for people of feminine persuasion.