Brexit or not the UK still has a lot of soft power, it’s still a G7 member and a large economy.
Other countries won’t look too kindly on a corporation ignoring a major and very well respected regulator even if their interests aren’t impacted by that particular decision.
The rule of law is something countries fight to preserve and it’s very much a collective thing.
If microsoft decided to no longer do business in the UK (not happening - it's a bluff) it would not be beholden to their decision.
It would be a different situation if either company was based in the UK, but that's not the case.
There is a very big difference between that and seeking permission and being told no and then acting like a 5 year old which is what Microsoft and Activision are doing.
Now any threats that they make are probably just bluffs, but there's no way that senior staff of a defunct division would be arrested for something done by their former company, and the idea that there'd be any extraditions going on seems unbelievably far fetched to me.