Well if the two US companies that do business in US and with US residents, than UK court would not have any jurisdiction. (And would not even try, it's not like they don't have other things to do.)

But in this case, you have two US businesses, that own local UK business and do business on UK soil with UK customers. That is why they fall also under jurisdiction of UK.

MS and Activison could close their business in UK, and stop serving their customers and then they would not be affected by UK courts.

Bottom line is, if you do business in multiple places, you need to play by the rules of all that places.

It's similar how the legislation in lets say California can affect products in all the USA.

Microsoft are free to withdraw from the UK market to avoid being regulated by UK regulators.

But unless they do, the UK has the right to regulate its own market in the way that they see fit, irrespective of whether that impacts on other markets (modulo international trade agreements).

The two US corps both want to do business in the UK. If the two US corps don't want to do business in the UK, they can feel free to ignore the UK authorities.

Presumably by banning them from business in the UK if they go through with it

It only relates to their activities in the Uk. MS would have to either comply with any remedial measures or just stop operating in there.