I would think that arrangement would work. I can't say if those channels allow use on more than one TV at the same time, so if the same channel offered two different games you wanted to display, it may or may not work. Perhaps they have something like Netflix, where you can sign up for a plan that allows more than one device at a time. Don't use them, so can't say.
Dan
Roku Stick (3600), Ultra (4640), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Nvidia Shield, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.