I feel for you and your children.
Treating a TV in the family living room as one person's exclusive property is not normal. A healthy relationship should involve sharing resources and making decisions together. It's not just about the TV—it's about respect, compromise and consideration for everyone's needs, including yours and your children's.
His refusal to allow anyone else to access the TV, even when he's not home, is controlling. Control doesn't always look dramatic or obvious—it can show up in small but significant ways, like someone dictating how shared spaces or resources are used.
He prioritises his wants above the entire family. This isn't how a partnership should work. You say, "No amount of talk or compromising is going to change anything". That's very concerning because it suggests he's not open to listening or meeting you halfway. A good partner cares about your feelings and is willing to make adjustments for the sake of the family. If someone shuts down discussions and refuses to compromise, they're making their way the only way—and that's a form of control, even if it doesn't look like what you'd traditionally think of as controlling behaviour.
He sits playing Xbox all evening and weekends while your children are sent to their rooms to watch TV, which they don't want to do. He is isolating them and depriving them of quality family time. It's so sad to think of you wishing for something as simple and normal as watching a film together and being told it's not going to happen. You deserve better than that.
This kind of situation can make it hard to see the bigger picture because it's easy to get used to it over time. But just because something has been happening for a long time doesn't make it okay. This isn't about you being unreasonable or asking too much—it's about having a say in your own home and making sure your children grow up in a space where everyone is valued equally.
You say he isn't otherwise controlling. I don't believe this, but I believe you may do. I'd strongly urge you to reflect on whether there are actually other ways in which he makes unilateral decisions or disregards your feelings. Sometimes these behaviours go hand in hand, and it could help you look at the full picture.
You and your children deserve to feel comfortable and valued in your own home. You don't have to accept this as your life.