Literally the best way you could bond with him nowadays. Keep doing what you’re doing hopefully she’ll see in her kid that you guys do have a bond.

It doesn't mean you are, either. Even so, it's a pretty lame way to bond when you live in the same house.

Have you tried to explain this to her? I agree with Rozay. This is a way you can bond with kids now. Probably she means “dates” such as taking him out to the skate park or trampoline park. Something that is more impactful. So he can see your gestures, see how you interact with society, get to hear your thoughts and opinions. So you can be someone that his safe space. Sometimes boys cannot turn to their mother as much as they could with a father.

quality time vs video games together should be easy to see the difference, sure you're playing the same game, however you're still in separate rooms not physically interacting. I could see it being a side bonding thing when the weather isn't the best out or you can't think of other ideas to do with him. Being outside, or doing real life activities will teach him bonding doesn't mean screen time, I don't know why people think this is good bonding when you're not even in the same room, and you or him might rage out, that doesn't sound fun or productive. to me looks like you want the screens to be the parent and not actually step in. i mean you even stated that's your wife's kiddo, not even trying to take on a parental label for yourself, just made him sound like the annoyance...

Sounds like an excuse for a third playstation to me.

so go outside and actually DO something with the boy that doesn't involve sitting on your ass. and maybe help around the house a little

Good on you for playing against your son. Maybe move the games closer together?