It is indeed a Ki-rin
Jeremy Crawford has stated in a Tweet as a response to someone posing this same question:
Casey White @CaseyDaWhite
@mikemearls @JeremyECrawford Not sure who to ask, but what is the familiar sitting on the War Mage's shoulder? (Pg 59 of Xanathar's) I've been pouring over the monsters and can't find anything similar.
Jeremy Crawford @JeremyECrawford
The war wizard in Xanathar's Guide to Everything has a special companion: a baby ki-rin! #DnD
Yes, they are normally huge but this is a baby one hence the smaller size.
As a small bonus, note how Mike Mearls was also unsure what the creature was prompting Jeremy Crawford to once again clarify:
Mike Mearls @mikemearls (Replying to @CaseyDaWhite @JeremyECrawford)
Good question - we don’t know! In the art review, we thought it looked really interesting, so we didn’t ask for a change. I suspect it’ll be a critter added to the game at some point.
Jeremy Crawford @JeremyECrawford
Mike, we worked with the artist to make it a baby ki-rin.