You may need to read the books Nyar appears in again if this is what you think, because just about none of what you just described actually applies to him.
Let me just go by my own criteria for a moment:
Motivations: In a verse where the gods are vast and powerful beyond reason and normally have little to do with humanity unless humanity comes looking for them, he/it is the only one of these gods to hold a vested interest in humans and the world in general. While most of the Outer Gods are decidedly neutral in terms of their aims and the destruction they might or might not cause, Nyar is legitimately evil and delights in sowing discord in every possible way he can, be it widespread or personal. He is a god who enjoys chaos, and is willing to pose as a mortal in order to see it happen.
Presence: Not only one of the few Outer Gods to actually show up in a book, but one of very few named Outer Gods to show up in multiple different works. As for in-universe presence, the truth about him is that he could be anywhere, posing as anyone. And while that gives him perfect anonymity as far as in-verse characters are concerned, to a reader, it translates to him being able to show up at any time without warning. This on top of being one of the aforementioned Outer Gods, who are already built up as major forces in the verse by the time we actually see him do something.
Threat Level: An Outer God who likes to walk amongst men, in a set of works that primarily feature Human level characters. I think that speaks for itself.
Personality: Aside from what's in the Motivations section, the one striking thing about him is that he's almost always showing up as a tall, thin and disarmingly happy person. (Or at least I remember that much) He's also not above gloating at times (as we see The Dream-Quest of Unknown Kaddath where he "taunted insolently the mild gods of earth whom he had snatched abruptly from their scented revels in the marvellous sunset city.")
Entertainment: I dunno about any of you because like I said I'm not sure how many of you people have actually read Lovecraft, but I was personally entertained by the few appearances he made in the original Lovecraft books. I didn't read everything he was in (not yet, anyway), but in the few I did, I definitely felt like seeing more of this malevolent, chaotic god who exists to sow discord amongst humanity.