Are microservices "cloud-ish medium-lived services"?
Are those typically "microservices" or is this something different?


"Cloud-ish" services could include microservices. I would include services that are replicated and/or load-balanced, such that you can sustain downtime on a single machine, VM, or running binary without service disruption.

Their differentiation of VM-like services looks like services which have a lot of local state (in memory or on disk) where frequent restarting would incur lots of downtime (from either the time it takes to boot/populate a new VM or because the service is singly-homed.)


  Would you put applications that scale on demand as part of those
  "cloud-ish" services, or would they fall into the "lightweight
  compute engine" category instead?


They could be in either category. Scaling on demand is a commonly-used "feature" of Cloud computing. Think of "Lightweight compute engine" tasks as things like batch jobs, manually run jobs, one-offs etc.