Originally Posted by a Master Ninja
NG3 = Ryu
NG3:Sigma = Ryu's shitty friends
how is that funny?
Ninja Gaiden 2, "This is a new story starring Ryu Hayabusa. It takes place after Ninja Gaiden 1 for Xbox, and before the timeframe of the old Ninja Gaiden games on the NES." -1up, James Mielke, 2007-11-16
Ninja Gaiden 2 Interview, "Story chronologically as well, this takes place after the fist Ninja Gaiden for Xbox, then after this, the story for this game from a chronological stand point leads into the old Ninja Gaiden for the NES. I think we have a nice continuity there." -Videogamer, Wesley Yin-Poole, 2008-05-22
Ninja Gaiden II: Q&A with Tomonobu Itagaki, "In story chronology as well, this takes place after the first Ninja Gaiden for Xbox and then after the story of this game it leads into the old NES ones, so I think we have a nice continuity there."-Gamespot, Luke Anderson, 2008-05-23</ref>
The creators confirmed that NG2 was a direct lead-in to the NES trilogy, i'm still not sure where NG3 fits in the timeline with this confirmed. This could be a case of Hayashi sticking the middle finger at the original trilogy while Itagaki respected it as he should.
The original trilogy is more important than you might think for the story.