It'd be useful for game developers also.

Bungie had to build an infrastructure to push analytics from Halo into their system so they could get "heatmaps" of where players were in a multiplayer map. This fed back into their design process and was used to tweak maps after release.

Building something like that might be easier if all the state is living in a cloud server "right next to" the analytics pipeline, with no need to push state over the external connection. It could, hypothetically, even be built as a library Google supports directly.

That's for sure, but Google wouldn't be Google if they don't invent the way to derivate from that data something like "neural heatmaps" of the particular user to use it for advertising part of business.

Not necessarily. Google doesn't derive advertising (or any other data beyond broad bytecounts, for that matter) from the cloud-customer data stored in their cloud storage infrastructure.