A Flock of Seagulls postdates the "classic" synthpop stage, but they also still exist in a period in which music which is retroactively called synthpop actually featured a fair number of non-synthesizer instruments. In fact, they were a regular band with a regular guitar player, bass player and drum player, while the lead singer was also a keyboard player. While many patently non-synthpop bands had pretty much the exact same line-up, A Flock of Seagulls were clearly New Wave and sound like synthpop, whereas someone like Journey, for instance, does not. Possibly the guitar and bass players simply weren't talented enough to "showcase" their performances, so they faded more into the background, making the keyboard elements appear to stand out in comparison.
Then again, bands like New Order had pretty much this same line-up too (although in their case, it was the guitar player, not the keyboardist, who did the vocals.) And Depeche Mode, who in 1980 and beyond for a few years, were an exclusively electronic band, now use an awful lot of guitars. In reality, synthpop seems to be a somewhat nebulous category of music, wherein music that sounds just like synthpop (like some work by Cher or Madonna) is not called as such, whereas music that doesn't (a la recent Depeche Mode) still is. Exactly how this came to be is not entirely clear to me, although it is clear (although I can't put my finger on exactly why) that A Flock of Seagulls sounds like the same kind of music as synthpop, even as it is heavily guitar-driven in most respects. In any case, here's "Space Age Love Song."