We say the game/war/party. is over, to mean that it's finished or stopped, but we say "Time's up" !

Same with Peter, I've NEVER heard "time is over" normally it is "time is up" maybe because it is easier and faster to say time's up.

Just to add, the word "time is over" is literally impossible cause time does not stop. :)

The only obvious reference I can think of is saying "time's up" to announce the end of something would have originally applied to any activity which had a time limit on  it. I've never heard of "time is over" only "the game is over".