there's a baseball game here somewhere and one here
ESL baseball game, conversational activity, printable baseball cards and supporting downloads
But with that number of people, I imagine it would be difficult to work in much English at all.
How about a categories soft volleyball game? Just have the server choose a category like colors, fruit, vegetables, actions, ... and each time a team hits the ball the player has to say a word from that category.
Since you have a large audience span, you might make it so that it's OK to repeat the word another player used.
Anyway, you could have a few games going at once and that ought to get most of your 'students' in the game.