The frustration caused by its difficulty, as well as its brevity, mean R-Type III will appeal only to a small niche.
The reason is that in the second level the difficulty increases dramatically, and keeps getting harder as the game goes on. That isn't to say the first level is easy; on the contrary, it's fairly difficult for all but a seasoned gamer. But very early in the game the difficulty passes from being challenging and entertaining to being hard to the point of frustration.
In fact, if R-Type III could be summed up in one word, that word would be frustrating. I relish a difficult game, but not a game so hard that I literally have to replay the same fifteen seconds of a level twenty times until I have all of my enemies' movements and firing patterns memorized so that I can go on. If you think that sounds annoying, I haven't even scratched the surface.
Oh, and there's another problem: this game is short. As in six levels short, the levels themselves lasting about five minutes apiece, not counting the numerous times you'll have to restart when your ship gets blown up.
I realize that both of my gripes with this game are common features in all shooters. That doesn't make this game any more worth the $8 asking price. Ultimately R-Type III is a very fun, even addicting, game, but that won't matter much after you give up on it due to the horrendous difficulty.