So to be clear I don't support restricting moves unless it is helpful in keeping the site from going down. I would only support it as a temporary measure. I notice you have only 20 games running, whereas I've seen some players with 400+ concurrent games, which basically means they must have moves to make no matter when they log in. While this is fine in theory, if it puts a strain on the server I would be in favor of limiting the number of moves.

iyt limits non-paying players to 25. This is miniscule and an attempt to get those players to pay, not to help performance.