Interesting music, they have a sound that stands apart from most others I’ve heard. Not your usual metal-ish melodic sense.
WARNING – Personal musings ahead… 
It’s also interesting how music (probably all art) impacts different people differently. In the final result it’s an inconsequential point because as Chick Corea put it, “There are only two types of music, good and bad.”
That song didn’t trigger the notion of “prog” in my mind at all. I’ve learned I tend to see the prog genre differently from what’s common now. Maybe that’s a result of coming out of 1970s music, including the birth of (mostly classically-influenced European) prog.
For example, Rush has never struck me as a prog band. They certainly had more or less, at times, prog influences – no doubt. But at heart I hear them as a hard rock trio with other stuff layered in, mostly, plus some wanderings into other stylistic areas over the years.
On the other hand, “prog” conjures ELP, Yes, Gentle Giant, Triumvirat, etc. There’s also King Crimson who were always – and quite deliberately – outliers. And yes, they’re all older bands, but that’s because I know of little (any?) current “prog” in that vein.
My perception of prog is music done by classically – or at least non-solely-rock – trained musicians, with some rock pasted on the outside. That was kind of the European way in the 1970s: classical core, rock skin. Whereas, the rare American “prog” was rock at the core with classical pasted on the outside: rock core, classical touches (e.g., Kansas). What I hear called “prog” these days is almost completely bereft of European classical influence, much less form and structure.
Please note, none of this is any indication of “quality”, plus or minus. Just idiomatic musings.
Anyway, enough of my rambling… 