I don’t play much, but if I do I pretty much exclusively use the deck or a controller… I don’t think there are many games that don’t support controllers, so I guess you could just check your favourite ones and see if they work well?

Games that I enjoyed on the couch more than on mobile or on the PC:

• tetris connected. It’s tetris, all right, but with lights and sound! Works so much better on a large screen and a sound sound system.
• redout (2). It’s a fast antigrav racer, bit like wip3out. Music of the first and sind effects and graphics of the second just work better in a home theater. Two stick controls are awesome.
• hellblade, if you have a surround sound system.

Apart from that, there are the usual suspects: 3rd person console ports (horizon, Batman etc) or couch coop games if you have some friends over (Bumerang fu, lovers in a dangerous space time etc).