Yeah, hardly any modern Prog band considers itself influenced by Fates Warning - which kinda makes the original all the more unique and indispensable. Sieges Even is the only band that comes to my mind, they've sometimes sounded HUGELY FW-ish in the guitar department.
As far as I can recall in those days, Fates Warning was the real first prog metal band, along with Queensryche a year or two later. Of course the term Prog wasn't used to describe it and we had Iron Maiden playing various rythm changes on their songs already, but Fates Warning kinda took the legacy from Rush's discography and adapted it to Metal, using some arabic or oriental influences on their first 3 or 4 albums. Things just started changing with the fourth album, "No Exit", and they "cleaned up" their sound, maybe a little too much for their sake, and then bands like Queensryche and Crimson Glory became huge and FW just stood in the shadow. But of course, that's the view from this side of the planet. Nevertheless, they are pioneers and worth listening to.