Is this guy a narcissist?

I've asked other qs here about this situation so sorry for the repeats. Have been really struggling to get over a situation and I think I may have cracked it: the guy is a narcissist. My dad is a narcissistic emotional abuser. This guy (who lived in my college dorm and also had classes with me) was not abusive but very manipulative (although could also be very sweet, generous and nice - to be fair - so can my dad to those who don't know him well). Let me know if you think he's a narcissist or just a bit of a shitty dude.

#1: Constant put-downs. He'd be sure to find out peoples' insecurities and then laugh at them. Even down to things that hetero men don't usually notice - like the quality of your hair dye or your type of shoes. He called one girl "irrelevant" and another "so boring I'd swap her for scrabble". Note that he always says it with a joking manner - so if you flag him up, he says he's joking and you're being too sensitive. It's almost always towards women.

#2: In spite of this he's actually really insecure with women. He brags about the number of women he's slept with (normally to me that's a red flag for someone who's actually sexually inexperienced - seasoned players would never brag like this), although I met a guy who went to school with him and he told me this guy was a virgin throughout high school.

#3: He flirted with me and only me at our college constantly and persistently daily for about 10 months. When I showed some slight interest back, without flinching told me it had all obviously been a joke - no apology whatsoever. He only got upset and slightly remorseful when I stopped talking to him to try to get me back again (he obviously liked the attention). But when I cut him out completely he told everyone that I was a "ho who threw myself at him" (completely untrue).
Is this guy a narcissist?
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