I broadly agree that "cloud" has an awful lot of marketing fluff to it, as with many previous buzzwords in information technology.
However, I also think that there was legitimately a shift from a point in time where one got a physical box assigned to them to the point where VPSes started being a thing to something like AWS. A user really did become increasingly-decoupled from the actual physical hardware.
With a physical server, I care about the actual physical aspects of the machine.
With a VPS, I still have "a VPS". It's virtualized, yeah, but I don't normally deal with them dynamically.
With something like AWS, I'm thinking more in terms of spinning up and spinning down instances when needed.
I think that it's reasonable to want to describe that increasing abstraction in some way.
Is it a fundamental game-changer? In general, I don't think so. But was there a shift? Yeah, I think so.
And there might legitimately be some companies for which that is a game-changer, where the cost-efficiencies of being able to scale up dynamically to handle peak load on a service are so important that it permits their service to be viable at all.