From what I can infer from the description of the game and three screenshots that were shared, the game appears to be running an upgraded Sigma 2 engine.
Ryu is seen slicing people with blood splatters all over the place in the dark rainy streets in the first screenshot. In the second, he is climbing up wall using a dagger, and in the final screenshot, he is seen running away from a giant spider like creature.
Among other juicy details about the game were the following tidbits. Ninja Gaiden 3 will be locked at 60 FPS. It would involve more blood and gore sequences compared to previous games.
Difficulty level won’t be adjusted for the casual fans. The developers want the game to be more difficult to keep the challenging aspect of the game intact.
Competitive and cooperative game modes supporting up to 8 players. Ninja Gaiden 3 won’t feature a store to purchase and upgrade weapons, instead the weapons will upgrade over time.
May be skill/experience point system would be implemented. It would be more story oriented than previous games. It isn’t confirmed but it may feature move support.
Ninja Gaiden 3 will be demonstrated on E3 2011 by Team Ninja. If you have somehow missed the teaser for the game, you should see it below.