Depends on the game really. If it's Forza Horizon 3, Gears of War 4 PvP, PSO Battle Mode I'm probably listening to some music. If I'm playing something that has a grind or doesn't take any skill/attention (The Division co-op, PSO Normal Mode , Gears of War 4 Horde, etc) I'll watch something on the big screen with my girl.
Edit: Couldn't find the playlist for the official channel on YT but here's the first episode of the series I watched with her while I was still playing PSO. Highly recommend watching Kill Bill 1/2 and having some slight C&C Generals, Zero Hour, and Halo knowledge so you'll get the neat little tributes they have.