Don't force him anything - paying rent or leave the house, for example. That could end really bad. According to one great podcast I heard, "if you want to help somebody, ask them what they need". So making him paying rent (etc.) is good solution from your point of you, but I think there is underlying problem. His motivation. I've experienced it myself. The right motivation makes you do amazing things and fills you with energy. And the urge to leave the house should come mainly from himself.
It's a long journey, but independent one, where your input won't be required in the end. I think, correct me if I am wrong, that if he would be advancing in life you would be fine to have him with you. The two reasons people leave nest on their own:
- finding a buddy they want to have privacy with and potentially start family
- home environment isn't sufficient anymore
ad 1) finding boyfriend / girlfriend is hard if you have no self-esteem, if you are not satisfied with yourself - basically the Maslow's hierarchy of needs . Also I find it easier to find people to increase their proficiency in whatever hobby they have. There are similar minded people for everything. That brings me to point 2.
ad 2) Find his points of interests, his dreams. He might not talk to you at first, he might not even know them. Get to know him more, encourage him to go after the dreams. Maybe try different hobbies with him. Also, if he plays video games, they can be just a runaway from harsh reality OR the hobby he likes. If it is his hobby, that's great, you found it and he can even make money with that.
If it is a runaway, I would give him more house chores and show him appreciation even for the smallest things - to show life doesn't suck (source for this and many other relationship hacks is this pastor's video , also I recommend the long version).
Myself, I have a hobby I wanna give every minute to, but know I have to do some adult things (like work, chores, etc...) first. So if they are not too big, I know I can finish them and still have time for my hobby. That's what really drives me - the passion for something. Find it and you will see him outgrow the house. And almost every passion is better than none. Gradually he will want to make things you don't allow him at home, things he wants to do differently - that makes him leave. Or he stays with you glowing with enthusiasm. Possibly also finds a soulmate in the hobby group around.
Lastly, stay kind with him, it might be beyond him.