This is what parents are for.  If the parents won't require a kid to do something, like going outside, the consequences are on the parent.  As the SO of the parent, you can only protect yourself and your marriage from any crap that may result from poor parenting decisions.

You are 5-ish years from the Skid launching and phasing away from your home.  As that starts, it is imperative that you keep putting fuel on the burning platform and decreasing the desirability of your home as a place for this kid to avoid the outside and more importantly, avoiding progressing into adulthood.

^ I agree. If their parents don't see a problem with it, then so be it. I strongly disagree with DH about screentime, but at the end of the day, it is his responsibility. And the repurcussions and negative effects it has on SD10 is totally up to him and BM.

vitimin d deficency and rickets are real. If he literally never goes outside I would have his dad talk to his doctor. Also agrophobia is a thing that I am sure there will be more of as we are coming out of these virus lockdowns. 

My younger DD35 was like this as a child and a teen, she'd rather sit in her room playing computer games than go out either for sports, exercise or socialising.  However she did improve and will now go out for runs and pretty much carries on a normal life indoors and out, so there is hope!  I think if you try and put pressure on him he will resist it even harder.  Give him natural vit D capsules.  

I made SS9 go outside today, because all he does is stay inside with face glued to a phone. I told him I need to clean and to hangout outside and because it's nice. He goes out there, with phone, few mins later ask to come in, I said why? He said it's boring? I told him I could give him something to do and help me clean.... he turned around walked right back outside. Mind you this kid has a basketball run, baseball net, electric scooter, a ton of games, he use to like to draw and has all this drawing stuff, books, and more. All this stuff he has and all cause he wanted it- yet DOESNT remotely play with anything. All he cares about is a phone. 
 

I made him stay out there and even eat his sandwich outside. I get a call from DH saying why is SS outside? I told him bluntly "I'm cleaning, he needs to get out of the house, if ain't hurting him. He can hangout and do the same thing that he'd be doing in here (on his phone)! Stop questioning it. You should be happy I got him out there. He has so much he can do yet he chooses to be glued to a phone. So he can do that OUTSIDE WHILE I CLEAN AND HES OUT MY WAY! Jeezus Christ. 
 

So SS must have texted him some bullshit and told him he's outside. Like what the fuck? Lol it's freaking gorgeous out and your whining like a little girl to come in. Hell no! Stay outside. Otherwise I'll put you to work inside hahahaha

If they won't go now, and won't be told to, then they won't go later and won't be told to...