It seems to me that the problem is not with the gaming per se, but with the fact that he’s not focusing “on the importance of his daily tasks”, as you phrased it. Unfortunately, that is the very problem with ADHD – the important completely loses to the interesting. Chances are that taking away the games will merely lead him to find something else interesting to do. Even more of a problem is when the important things are important just for you and not for him. It’s not that he doesn’t value that, it’s just that his brain never gets a chance to panic in that case, and use the resulting adrenaline rush to get him started.
DH and I are both ADHD, and only when our kid got diagnosed we realized that most other people would be able to easily select important over interesting. It seemed so magical! So my only suggestions are shared calendars, reminders, always enforced hard limits on time-constrained issues (no pulling out the phone at the table, no going away until dinner is finished), picking your battles on minor issues, letting him fail on things that only concern him (it’s how everybody learns), and most of all try to let go of judgement, because nobody is likely to do well when they feel judged. What he does or doesn’t do has no bearing on you, although I understand it can be hard to see that (we had our moments also).
Now, if the guy grabs the game from the kid and goes crazy shopping, like for that other poster (hugs!), that’s past ADHD and getting into addictive behaviour, in which case he needs professional help. I’m guessing that’s not the case here, although I suspect an ADHD coach can help.