yes you are wrong... a 5 year old should be able to entertain themselves for hours.... nothing wrong with it...
if DH has to entertain her every minute he's at home you will complain in 10 years time... cause by then SD is to old to learn how to entertain herself... be glad she's not the point DH revolves around...

Simply do what you want and if you go out for a couple of hours... DH is there for supervision, so far SD has not hanged the cat or burned down the house, you are not there to see if DH gets up and gives her a snack or something to drink, thus stop stressing.... they are fine and you are getting a little independent step daughter

I have a 5 year old. Mine is capable of independent play for maybe 45 minutes. After that, she will come looking for me to ask what she can help with or if I'll come play Shopkins with her. 3 hours is a long time for a 5 year old to be left to their own devices.
There are days where I feel a little blue. There are weeks where I'm stressed. But I have children to raise. I don't get the luxury of checking out on them. Unless a parent has some serious mental health issues, checking out on your kids is selfish. We'd all like to have more time to do frivolous fun things. It helps us relax. But 3 hours a night, every night? That's not okay. I think his daughter needs to go back to her mom (unless mom is a train wreck as well). I'm sure your husband is a as nice as you say but he is not being a good father right now. If he's not willing to unplug the game or seek help for depression (if that's what it is), your stepdaughter should go to her mother.
I see nothing wrong with the healthy boundaries you have set in place.

Let him know he can play if he wants but to take breaks to spend with his kid. I get it, I really do. I have chores/errands to do that takes the better part of the day and don't have as much time to answer every single one of DD3y/o's bid for attention (I have to do it for DD4months because, well, she's an infant and her needs are a bit pressing.) But I take short, few minute, breaks to interact and play with DD. DH also works when he's home too and sometimes he'll be at the computer for a few hours--I just gently nudge him and say, hey I think DD3y/o misses you, could you lay with her for 5 minutes? Or I put DD4months into his lap and tell him she wants to get to know him for a few minutes and then I take her away.

Have your DH set up things for the SD to play with at different intervals (like get it ready before he sits down to do his game--first box has clay, second box has watercolor paint, then third box is actually educational TV time). We have a crafts box full of things to do that she normally doesn't get to do, like clay and stuff and it can keep her busy for quite a while.

I've had this problem sometimes with DH and SS5. We will fight about it or talk about it before going to bed. I tell my DH: "your days of playing Xbox whenever you feel like it ended the day you decided to have a child. SS is five now and all he sees is you playing your Xbox so what memories will he have when he's older? I know you didn't have a dad growing up but you need to be the dad who was around and being on the Xbox for hours on end doesn't cover it. I don't care that you are stressed, everyone gets stressed out and the world doesn't stop, your parent switch doesn't get cut off because you can't compartmentalize work and being a dad. If you don't want to play with him to his mother's because even if she doesn't want to play with him after her long day at work at least she lives in a neighborhood where he can find other kids to play with."

Obviously you need to change it around to fit your situation but this has given me the best response. I didn't raise my voice, I didn't argue; I don't him the truth and let him simmer on it that night. Now he plays with SS or BS in their rooms doing puzzles, cooking together, playing outside or going to the store one-on-one.

Sunshinex, what about your DH setting up a timer to go off after a certain amount of time? Give SD an activity with an idea of how long it should occupy her, say, 45 minutes. DH can set up a timer to go off after 45 minutes to check on SD.

NOT outside. I do not believe a 5yo should be outside alone and unsupervised.

DH has mild depression and ADD and it's worse in the winter.

He goes through episodes of being totally withdrawn from both me and the SDs (no more than a day or so). He'll be on his phone or computer compulsively - even when we're watching a movie he'll be on another screen and not paying attention. The SDs are better now about letting him know "Hey dad that's not ok!" as they are older, but I do think some of their issues with "responsibility" and learning basic things are party due to his reticence about doing the basics and energy levels. Parenting is hard and draining and more so for him at times. He's admitted this.

And that's very difficult to navigate - I do help when needed, but have had to put strict boundaries about how much I do and what I do. He has to learn to put down his device and engage or at least try to do something new. Since I withdrew several years ago from planning things for everyone nothing is done. He'll complain, but I just nod and tell him, "Well, you can go ahead and plan something if you'd like, let me know what it is if you need input." But he has to do the work.

Have you discussed this with him? DH and I talk about it, he's very open with me and I have no fear in pointing out what's going on, or not going on. Does he know he's depressed? Has he received help for it? You may have to decide how much you can take on and what you are willing to do. I would hope he appreciates your help (this I have zero doubt about which is the saving grace of my time).

I'm probably showing my age here - but I would have a bigger problem with a grown man playing video games for 3+ hours a day and ignoring everybody. Does he know he has issues with all this? - the video gaming, ADD, and depression? Is he willing to have an honest conversation about it and to seek help? If not, not much else you can do about it. I kinda feel bad for the kid tho...

My kid was apparently a mutant at +/-5yo and would spend hours playing quietly by himself. Every once in a while he would take what we called "roll call" and call out "Mommy, Daddy!" to which we would both respond with "Here!" and he would go back to playing until the next roll call a couple of hours later. When he was a toddler his mom and I were in school and studied much of the time. I was in grad school and his mom was working on her undergrad.

He was a liner. He would dis-assemble his coloring books and line the pages up as paths throughout the entire house, he would line up his cars, he would play with blocks, he would disassemble the dry cleaning hangers for slacks and turn the cardboard tubes into all kinds of things, swords, shields, etc.... He would spend hours "reading" and as he was learning to read he would sit on the floor in our kitchen recreating the words from the books with the letter magnets on our fridge. I started that with him when he was a toddler and he would do it on his own working out how to read on his own initiative.

I think this kids not being allowed or able to play alone and entertain themselves thing to be a major parental failure in today's parenting circles. Kids who require constant engagement and external stimulation will likely struggle being self motivated as young and then full fledged adults.