It’s not. It’s a very, very twisted ending--Jinkuro agrees to alter his fate by not attempting to kill Yukinojo at that very instance when he’s meeting with Momohime, and we’re left to expect he’s accepted his inevitable death by the hand of his illness. Instead, he fools Momohime into thinking he died from the illness while, meanwhile, killing Yukinojo and taking his body. After all, there was nothing that said Jinkuro couldn’t kill Yukinojo at all--he just couldn’t do it in that original instant.
Momohime notices Yukinojo is acting uncharacteristically antagonistic lately, but Jinkuro never reveals his true identity to her (there’d be no point, as at this point the timeline has reset so Momohime had never known him), and continues to live his life through Yukinojo. Momohime lives to the age of 100 with three children, meaning that Jinkuro continued to deceive her all those years. On top of that, Jinkuro doesn’t try to alter his behavior to be more like Yukinojo’s, thus being granted a new “chance” at life--no, he gleefully seizes the opportunity and continues to go on his killing spree ways. This is the ending where he has his cake and gobbles it down too.
It was a pretty unnerving, Twilight Zone-esque of an ending, especially as it ends with Jinkuro in Yukinojo’s body laughing maliciously. It’s funny, because for all his callousness I never really considered Jinkuro to be that much of an outright villain--he’s remarkably capable of showing remorse and sympathy, and his serious crimes (apart from killing, which is par for the course in this game) aren’t really spelled outright to us; plus, we see him giving up his life for Momohime twice, leaving us with a surprisingly positive impression of him. But here, when given the chance to live, provided that it doesn’t risk Momohime’s life, he’ll absolutely take it--and he won’t rid himself of his true nature in the process.
I wonder how much of it ties back into the game’s Buddhism themes, though I don’t think I’m anywhere near qualified to discuss that. I bring it up, however, because Torahime’s story is about her (after having died and been granted by Buddha extra days to live) achieving enlightenment, and how she’ll be unable to attain it if she returns to the living world. Is Jinkuro’s story, perhaps, a darker mirror of that?