I think this might be a remake not done by the same people who made Advanced Ninja 1. I think the real sequel is this game:
Advanced Ninja 2 By Sam Clifton. It really captures the game-play of the first. I am not sure what the other 2 and 3 sequels are about.
What is looks like is that advanced ninja 3 is the last one. If you go here and read the comments (I know the screenshot looks awesome). Anyways, it looks like he can't seem to finish the new game because it is too big and he losses interest quickly. He may never finish it. I say, give him words of encouragement. Advanced Nina is a great game.
Not by the same people but really fun and similar gameplay: Double Wires