When I say "fundamentally a web game" I just mean in a technological sense (written in javascript with UI elements in HTML), rather than some sort of genre sense. Genre-wise, it's a point & click adventure, albeit a fairly simple one because it was made for a jam. Not sure if that falls within your expectations for "web games" or not.
I feel like insofar as "web games" have identifiable genre characteristics, it has more to do with them typically falling into one of two categories (either non-commercial hobby project, or commercial but casual f2p game) for economic reasons, rather than anything particularly inherent to the web as a platform?