Disclosure: I work on Google Cloud.
There are arguments on both sides about "Should Office count as Cloud revenue?". We have the same decision regarding GSuite. If you take the "Cloud is anything a business depends on" argument, then it obviously should count (but then all sorts of things like SaaS would count).
I like to think of this from an investor's standpoint: what do they really want to know? In my estimation, they want to know about potential hyper-growth market opportunities for the company.
For Microsoft, more than anyone else, Office isn't a high growth opportunity. There is some amount of revenue uplift from customers "upgrading" from Office on prem to Office 365 (like Adobe when they forced Creative Suite to be subscription) but I doubt there are going to be lots of net new customers just because Office is on a subscription model. By contrast, Cloud infrastructure is a large opportunity for Microsoft.
For Google (and to some degree AWS), "productivity suites" is actually a reasonable growth market, particularly as market share often comes from Office. However, the raw productivity market is still "only" $XXB (it's predominantly $X/seat, and there are only so many employees in the world) while people talking about "cloud" usually are talking about the opportunity being "all money spent on IT".
tl;dr: I watch the YoY "Azure growth was XX%" numbers and ignore the headline revenue.