Ulysees, My parents were divorced when I was tiny. Throughout my young childhood my dad picked us up every sunday. A lot of the time we just sat in front of the TV (my mum didn't allow the TV and there were no playstations!).
You could say that we didn't really have a relationship, but he stuck with that routine - every Sunday with him. As we grew older, we started to be ready to have more of a relationship and he was just there, so we could transition to that fairly naturally.
I think it's hard sometimes for the absent parent, as there is the presumption that because time with them is limited, unless they are doing something very involved they are 'failing'. But in a relationship between parent and child at certain ages it's normal for the child to just do his own thing.
The fact that the parent is in the background matters to the child, even if it does not seem to. Particularly if there is an abusive relationship in the maternal home, that time with dad may be a haven for him.
It may take your ss a long time to be ready to bond with his dad. All your dh can do is make sure he is there when his ds needs him.
In the meantime, just let him play on his ps - hang out nearby reading a book or whatever. Companionably sitting with each doing their thing is fine. They may even want to play some of the games together (but only if both enjoy it).
Sorry that was an essay! hth.