Neither of my boys have ever been aggressive. That's not necessarily a hallmark of ADHD.
We kick them outside to play. And play hard. Outdoor play is something that ADHD kids NEED. The less structured and supervised the better.
Of course my AD/HD kids hyperfocus on technology. But I take it away and make them go find something else to do. Be firm "Go play outside." or, if the weather is too bad, "Go play in your room with your toys." Or, "Go read one of those books we got from the library."
I've found that technology does tend to make them act up (though I don't have the aggression issue, as previously stated). They backtalk more and don't want to do anything else. So we only allow games on the weekend, after all chores are completed to standard. NEVER do we use games to calm them, and never do we allow them on schooldays.
I think you're setting a very dangerous precedent by using the games to calm him. "If I act like a little sh*t, mommy gets irritated and gives me the game I want." It's a negative feedback loop and you just need to stop doing it. If he's acting like a sh*t, send him to his room or outside....because his need for stimuli to focus on is not being met. So send him to where it can be.
Best of luck!