How to be sure he's studying not playing computer games?

I like computer games, but when I study (homeschooled) I use my PC. You've got to trust him. I'm 13, so you'd think I'd sit on my High End rig all day playing games. I don't. Sometimes I'll play on it when I have my break or after I've done everything. Just keep a small eye on him from time to time. Come in and help him if necasserry.

My answer would depend upon how likely you think he is to slack off..

If he usually requires little supervision for traditional homeschool assignments, then I'd simply check his assignments when they're completed. If it helps, give him a schedule. Give him a due date like he'd have in a high school or college course. You don't say if its an online course or curriculum, but if its a course, there's probably a pacing guide. That'll help him learn to meet the dates college and work will demand.

If he's prone to slacking off, or starts taking too long to complete assignments, then supervise him more. You could insist he do his assignments in the common areas of the house.

A certain level of trust us always better than micromanagement. It will help him to become more independent. Also keep in mind that a certain amount of games time is not a bad thing. When you need a break, you spend time on YA. it's not that different. Teach him to do the things you do when you're procrastinating or goofing off. I put away my tablet and phone. Pull back if he needs it.

Lot of way

You could tell him to study in front of you. For example, you were in the kitchen, just make him study in the living room so you could keep an eye on him. Or look over his work, after he finish study ask him some question to check if he got all the correct answer. Or, change his computer password without him knowing. I'm a dad, when my son or daughter not working or doing their HW, what I could do is to unplug the wifi cable. Easy.

Just help him that's all. He probably needs someone to tutor him anyway...chemistry can be very hard especially.

put the computer for school in one room and game consoles in another. i.e. the homeschool computer is downstairs in the dining room or something and the consoles are in his room... or you could look into non-computer homeschool.

How can you be sure he is sleeping at night?

How can you be sure he is not smoking dope?

How can you be sure he is not having sex?

You have to trust him sometime.