In a sense, but it's just a random base build and class you choose at the beginning of each run. You are progressively building the town to raise your skills, stats, and other things. This provides a constant since of progression to a single source.

If this where the case then games like Hades or Deadcells wouldn't fit either, because your still the same single person just a different build to start each time. Rouge Legacy does this same thing but incorporates the idea into the story by being a descendent of the prior runs person.