Your partner's the stupid one here. What sort of responsible parent allows a 5 year old unlimited screen time, on their own, shut away in a room with barely any other interaction ?
There's a time and a place for screen time .... it almost sounds as if he wants his son otherwise occupied, i.e. the screen acting as "babysitter" so he doesn't have to go to the effort of actually being a parent and involving his son in a variety of different activities and normal family life.
He must be incredibly lazy and/or have a very low opinion of himself if he really believes the console is the only reason his son wants to come over. Notwithstanding the fact that suggests that this extremely young child actually has a choice in the matter .... so what if he objected to coming over should his screen time be reduced, tough, he doesn't get a say in the matter at that age.
Frankly, your DP is being pathetic and irresponsible. And obviously, you're going to feel resentful at having no say at how the children (i.e. both of them) are treated in your own household - but I bet you are good enough to cook and clean for his son aren't you, even though your opinion re: how he's being raised is apparently "stupid".
Does he even want to see - I mean literally see his son ?
As others have said, time restrictions for the console are the only way forward. That, and you effectively detaching and doing what you want with DD - for now. As you say though, there may well be potential problems as she gets older and wants to do what her brother is doing. That's why it's vital that you and DP thrash out an agreement on gaming - so equal rules can be applied to both kids. And him suggesting that, for example, DD also gets her own TV and console and unlimited play on it when she's 5 as well is not the answer. Unless he effectively wants to shut her away as well.
Maybe you should dig out some research on the ill-effects of too much screen time upon kids - especially at such a young age. He can't just dismiss your opinion on this - it's very contemptuous. Also hope he's playing age appropriate games ?