He is old enough to learn "no." When he does something you don't want him to do, remove him and tell him "no," and provide him with an alternative. "No, you can't play on the computer, but you can ____." Expect to do this a lot.
You challenge is to hold the line with this despite whether he likes or doesn't like it, and regardless of how comfortable or uncomfortable it is for you yourself. It sounds like he has a lot of freedom to explore and do what interests him, so a few things that are off-limits are not going to damage him!
With my girls, I always try to keep in mind that my job as a parent is not to please them or placate them. It is to teach them the skills that will help them to be happy and productive and helpful members of society. Certainly, two of those skills are following rules and accepting that certain things are off-limits.
The tools that you begin to provide to your child now will serve him as he grows up and throughout his life. It is not easy to tell a child "No" -- especially when it has been a long day and part of your brain tells you to capitulate. But think of it this way -- would you let your child hit another child because it made him happy? Of course not. You would tell him "No" regardless of how it made you or him feel. And in doing so, you have just given him a tool that he can use for life.
Think about the long run as you have these questions: i.e., "In the future, will this help him?" If the answer is "no" then don't let him do it now. You are in a time when he is forming the foundations of adult behaviour, and laying a strong foundation -- both through your messages to him verbally and through your actions, is the most important thing you can do for him as a parent right now.