By the time I got there they were playing it.From your "thoughts" (had already played?) I gather that The game was already over.
Do you really mean this?
Got it. Thank you very much.In that case The game was already on is possible.
I would not use on myself, but rather The game was (already) under way.
But that might just be my personal preference.![]()
Got it. Thank you very much.The expression Something is on/off often means that a decision has been taken to hold an event (or not).
So we say The meeting is on (=will take place) or off (has been cancelled).
That is why I would avoid using on in your context.
Got it. Thank you very much.Another option is "the game had already started/begun."