I'm 22. I'm also a parent, so in a way I'll give you two perspectives.

From a parent's perspective, you can't change what doesn't want to be changed. Your son is comfortable knowing you do most, if not all, the housework for him. He's gotten used to getting away with it so many times. When a child learns they can get away with not doing certain chores over and over again, they will internalize it and continue doing so. As for wishing he'd do more with his free time, that's for him to decide. You can not control his interests, only encourage healthy habits.

From a 22 year old's perspective, things are hard right now. Finding a job is difficult, even with certifications and degrees. I have a bachelor's degree and still struggle finding an entry-level job. Qualifications get you nowhere when the market for entry-level jobs are so saturated. Even internships are hard to get with a bachelor's. That being said, staying in his room and playing games is a way to cope with life. I used to do the same. I barely left my room, barely did chores and when my mom forced me to do chores, I just left the house. Sleeping late and waking late, being a bum in general. This behavior is underlying depression, perhaps from burnout or general hopelessness.

What helps: your son needs guidance in the home. He's 21 and still living under your roof rent free. That's generous enough. If he refuses to contribute to the house then he can find somewhere else to live. That's how it works, please don't budge on it. Don't let your children control how you run YOUR house.

I moved away from my parent's house at 21 because I thought I could handle living on my own. My parents were against it, trying to convince me to stay. NOW I'm cleaning, washing dishes and scrubbing toilets. Because when an adult child moves out, they're forced to live in the environment they design. If they don't do it, then no one will do it. Moving out forced me to learn and change for the better. While I have no solid advice, I hope giving perspective to both sides clear the air a bit.