We have a set limit for screen time, rather than for specific, console/pc/laptop/phone.
Ds is 10 and has AS and he lives for computer games, but is still limited to an hour a day on a school day and an hour and a half at weekends and holidays and that includes all screens bar TV, which he's not all that fussed about anyway.
Could you possibly give him a set level of screen time, but enable him to earn back chunks of time by spending time doing other things?
Ds1 has an Official Nintendo Magazine subscription and is happy to read that and likes predictable book series (like Beast Quest) which can keep him quiet for a while. I also make sure he gets outside for at least a short time every day. He moans like crazy and there's usually a big argument first, but he enjoys himself once he gets out there. He's recently even started throwing the dogs' toys for them and when he gets into that he forgets to moan and ends up staying outside longer.
Ds doesn't really do toys either. He likes beyblades and ninjago, but won't play unless he has someone else to play with and unfortunately his brother is now old enough to vote with his feet when ds has been rude to him for the umpteenth time in that day (that'll be every day then).
He also likes the Lego Starwars kits and has very recently started making up his own models from the general lego basket (something he's never done up until now).
He really can't cope with unstructured time during weekends and holidays, as he finds it impossible to decide what to do and it causes him massive anxiety. To get round this we try to keep to a rough schedule, so we have meals at the same time, computer/screen time at the same time and as of next week he'll be doing a typing skills programme, plus half an hour of grammar and punctuation a day - for which he will earn a new Lego Starwars kit in the last week of the holidays.
I think a lot of children who have ASD struggle with the thought of a whole day stretching out ahead of them with nothing planned and no defined parameters, iyswim. Applying a semi-schedule definitely helps to keep ds calmer.
I think it might be a case of being stricter on the screen-time rules and having to grit your teeth and weather the moaning for a while, while you come up with some ideas for things he'd like to do or places he'd like to go. You might find that once he can separate from constant minecraft he is more able to think about the possibility of doing something else, but there's bound to be a negative reaction at first.