The problem is basically distributed cache coherence. You have many small data objects shared between a large number of machines. Often, one needs access to an object on another machine. How do you do that efficiently.
Spatial OS seems to work kind of like a multiprocessor cache.[1] Two machines can have read-only copies of an object. If one copy is changed, the other has to be updated. Performance is better if you don't have to do that too much. They use the fact that they're representing a 3D world to advantage. If something is geographically nearby, they try to keep it on the same machine. To load balance, they will cut up overloaded regions into smaller regions and apply more machines to them, or combine underutilized regions to free up compute resources. This is a rough understanding from reading the documents.
No idea how Hadean does it. The site doesn't say much. It's one of those "onboarding funnel" sites - no info for you until the marketing people have all your info.
[1] https://en.wikipedia.org/wiki/Cache_coherence#Coherence_mech...
I suspect Hadean is similar, they've listed Microsoft as a partner, and presumably it's a cloud service that they are offering, so wherever they host it is where you get it, you're never directly dealing with the cloud provider or it's billing.
It's plausible, arguably, that both could shift to alternate cloud providers if they wanted, but I get them impression their customers have no choice in the matter.
Also, they do get a little further into the weeds, but it's hidden behind a hamburger menu: https://www.hadean.com/developer/how-to-get-started-with-aet... though a code example without access to the library or cloud service isn't a whole lot of use for testing out!
Search with keywords "improbable google deal". First result [1]: "Improbable is also announcing a strategic partnership with Google, the first part of which will see Google providing its Google Cloud Platform as the backend powering the service."
https://techcrunch.com/2016/12/13/improbable-teams-with-goog...
https://www.hadean.com/ is presumably a direct competitor to SpatialOS then, I take it? And it's tied to Azure, I believe.