"Don’t be fooled: Microsoft’s cloud business is not bigger than that of Amazon’s AWS, although that’s the immediate implication."
Yes it is. And growing faster. And is profitable.
"Also, Amazon comes at this as a purely infrastructure-as-a-business, while Microsoft is offering this with Azure plus software-as-a-service with Office 365.
You need to therefore take Office 365 out of the mix and compare Azure to AWS. Here, the race is cheek by jowl."
No, SaaS is still "cloud". The fact remains that Microsoft are way ahead of Amazon in cloud revenue.