In a sense, no, he doesn’t. Because he isn’t.
However, his entire character is very typical of a ninja-like character in fighting games. His gameplay and looks reflect that. I would personally have him embrace his Tibetan monk side more, and I think his current looks do that, however, he also still reflect that of a ninja.
He’s not a traditional ninja though, not by any sense of the word. He’s not a shadow assassin of any sort. He’s a warrior monk who channels his chi through his attacks and can even use it to summon a blast of fire from his very hands, which are typical fantasy monk traits.
But again, compared to other ninja-like characters in fighting games, such as Scorpion and Sub-Zero from Mortal Kombat, whom Jago are inspired from, he does indeed fill the “ninja” spot on the roster.
That said, if Iron Galaxy can come up with a ninja design that reflected ninjas in a more traditional fashion, having a unique moveset and unique weapons, maybe being more of a shadow assassin, using stealth-like moves, illusions, smoke bombs, caltrops, shurikens etc., then I would definitely be on board!
Take Blazblue as an example. They have Bang Shishigami who is dressed in a garb that reflects that of a traditional fantasy ninja, however, most of his moves are very flashy and his personality is very… loud. He’s the typical fighting game ninja character, like Jago is, like Scorpion and Sub-Zero…
But in the newest Blazblue game we get Hibiki Kohaku who is more like a traditional ninja, using the shadows to his advantage, using illusions to play tricks on his enemy, yet is still stylish in his moves without being too flashy.
So like Jago, Bang initially filled out the “ninja” spot on the roster, but Hibiki is an alternative ninja design which reflects the more traditional kind of ninja. And I see no reason why KI can’t have that as well.
HOWEVER!!! One would argue that Sadira fills that spot, as she is a more shadowy assassin character, though not reflecting the traditional Japanese ninja, she still shows alot of the same traits as one.