I'd say it really comes down to whether your actor or microservice has any statefulness or if it's idempotent.
If you have a database behind your microservice, or some kind of in-memory cache, where you ever modify values instead of just writing and reading them then there's a good chance it's an FSM. On the other hand if it's purely functional - say, it just returns a thumbnail image for any photo you give it - then it's not really an FSM.
From what I've seen an awful lot of microservices out there have some amount of state (not sure about actors). I think that's why the author made the generalization.
You can make services and actors which can be modeled as FSM's but they don't have to be.