TL;DR:
I have a recumbent exercise bike, and have found I can play 4X-style games by having my mouse situated on a nearby table. But that won't work well for action games, nor for games that require a keyboard or flight stick.
I've looked into building a sturdy shelf for keyboard + mouse, to pair with a recumbent exercise bike, but all the newer bikes seem to have a control console where the keyboard/mouse need to be. (My backup plan is to modify one of these bikes to move the control console off to the side.)
I've also considered console gaming, because the controllers tend to be wireless and handheld, but I don't think they'd hold my attention as long as the games I care about would.
I'm personally limited to recumbent bikes because of back issues, but upright bikes and/or treadmills are interesting as well, because family members.
EDIT FOR CLARITY: For my personal use case, I don't care about the entertainment being in synch with the bike. I've just found I can bike for far longer if I have a computer game to prevent tedium.