How about no "sexy time" unless he fills out 10 applications a week and limits gaming to 10 hours a week. Want more gaming, fill out for apps. Want sex, get a job.
I think that would backfire. I've used video games to escape before. They are immersive and easy to get lost in in order to not deal with issues in life that have been internalized.
Much of those internalized issues involve guilt and shame, denying sex as a form of 'punishment' won't be an incentive, it will further amplify the feelings of shame and guilt, reinforcing the emotion that drives his desire to escape. It could be depression, or something else. Don't try to diagnose it, but try to figure out how you can redirect him without reinforcing any guilt or shame he may be dealing with.
The hard part is he needs to identify why he feels the need to escape. He may not be ready to face that head on. But you can try to replace the escape with something else that helps him feel rewarded. Is there something you both enjoy doing together that you haven't done in a while? Plan it out and go for it. If you can't compete with the escape, find a new one you can participate in together. The more connected you can get with him the easier it will be for him to open up to you. Sometimes just being able to identify the feelings and talk about them help.
As an example, my sister in law had been gaining some weight and was feeling depressed. Her schedule had changed and she wasn't taking the dog for long walks like she used to. That lack of exercise was replaced with 'mood eating'. My brother noticed this and kept encouraging her to take the dog for a walk. But that just lead to fights and she felt like he was telling her she was fat and to go for a walk.
He needed a change of plan. I suggest he take the dog for a walk and invite her to come with. She said no the first couple times. I told him not to get discouraged, just enjoy his walk with the dog. He started to like his time walking the dog, and he would come back and both he and the dog were having fun. Eventually she saw this and feeling like she was missing out started to walk with them. It wasn't about being 'coerced' or manipulated. It was about them doing something together and getting enjoyment out of it.
That of course doesn't directly apply here, but hopefully it gives you something to think about that perhaps you can try to apply in a way that works for you.
Good luck, I know from personal experience how difficult it is to walk away from using video games as an escape.