In my opinion it is a bicycle. 2 wheels? check. Human powered? check. Foot crank operated chain drive? Check, just a little more complicated than usual.
I don't see what whether it has a seat or not really has to do with anything, besides the fact that some make the baseless assumption that it's lack of seat makes it not a bike...just because of the wording of some laws. This is pure silliness. Is a bicycle with the seat removed no longer a bike? Modern BMX saddles are basically vestigial at this point, only being used as a holding point for some maneuvers and maybe sitting on while waiting ones turn to perform a trick over some obstacle. Apperently they have even done away with seatposts: The seat bolts directly to the frame. I don't think anyone would argue that BMX's are not bikes though.