I would certainly find it understandable but odd to read, "Scenery Spots" (as you found it on this web page.) "Scenic spots" is what I would expect. "Scenery spots" sounds vaguely like a stain on the landscape, akin to "carpet spots."
I think the website you cite is simply pointing out places ("spots") where beautiful scenery may be seen.
"Scenery spots" is never used in BE. It sounds like a rash afflicting those who have been out enjoying the scenery. "We've had a wonderful day, but we got covered in scenery spots!"