Team Ninja has not abandoned the Ninja Gaiden franchise proper, as the studio is already thinking about the next entry in the series.
In a video featuring Team Ninja boss, Yosuke Hayashi, and Yaiba: Ninja Gaiden Z creator, Keiji Inafune, Hayashi confirmed that a more traditional Ninja Gaiden is coming, saying that "Team Ninja is thinking of the next Ninja Gaiden."
"For example," he went on to add, "if the games were food, the Ninja Gaiden series would be a rich meaty entree and Yaiba: Ninja Gaiden Z would be dessert. Every course of the meal would be in the same Ninja Gaiden world, but gamers will experience different kinds of play. That’s how Yaiba: Ninja Gaiden Z will be different."
I don't know about you, but if Ninja Gaiden III was a meaty entree, I can't say I came away from that experience feeling particularly full. Hopefully the team will be able to get the franchise back on track with the fourth game.