Yes, every game can have it's own point system. The game admin can set the point system for the game from the admin portal. You can set a different point system for each of the 4 player categories.
The point system as set (available) at the start of the first lockout period on a game is fixed for the duration of the game and cannot be changed/edited any further by the Game Admin (or MyClubtap).
You can also activate the Grade Point System premium add-on, which enables you to set a different point system for each grade, which means each team linked to every grade can have a different point system.