you can shift to other games in the same genre if you need to put leverage on a particular company that is being irritating.
For one thing, a lot of skills won't transfer, especially the need to re-learn how everything is balanced. It'd be like trying to switch from Tetrinet to Puyo Pop or from baseball to cricket or from soccer to Gaelic football. For another, once a league switches to a different game, how can the league be sure that the new game's copyright won't get sold, such as at acquisition or bankruptcy, to another "company that is being irritating"? I can't see any way other than making sure the game is free software or has some other sort of irrevocable guarantee of non-interference with public performance for profit.
the issue there is more about people making money off the league