A possible scenario is that Sony has been floating this for a while but MSFT has resisted.
MSFT probably agreed to go in giving Sony good terms because they are afraid of Stadia. Not because it’s a threat to their gaming business but because it’s a threat to Azure. Heavy Stadia use means GCP has a high use tenant that pays for their use which they can use to make the rest of their offerings cheaper without losing profit. And that would hurt Azure, which is gonna be huge if MS is gonna live up to its trillion dollar valuation.
IOW they are worried that Google Stadia will be to GCP what Amazon retail is to AWS.
The article says the deal has been in the works for a year, the stadia announcement might have helped finalize it but does not seem like a first cause.
IMHO the deal is mostly coming from the fact that managing data centers is a mess, and MSFT managed to convince Sony they could do it better and for less money.
You can't really refute the actions from these companies themselves; they speak for themselves.