How to supply air in 2 rooms through a single joists cavity?
Without being there to visually see just what you have to work with is almost impossible. Try looking at an 8&quot;X 6&quot;X 6&quot; WYE duct at Lowes, Home Depot, or on-line to see if that will solve your problem. Can't think of anything else without being there. Don't forget to add a return air grill mounted near the floor if you want to add heat to the game room.
One possibility would be to install a heat duct for the game room and a small electric wall heater for the bath room. A better drawing or even a picture or two would also be helpful.