Chaos Incarnate

Inflated self-esteem or a grandiose sense of self-importance or superiority

He quite literally is a prince, so his claims of superiority are just as likely to come from the same skewed viewpoint Thor shared before Odin literally humbled him by banishing to Earth. When you strip him past the act he puts on, both in Avengers where he is quite literally mind controlled so that his envy and rage are exaggerated to Thanos's benefit and when he is defending himself in the sham trial Odin gives him in DW where he literally asks for the axe to end the conversation, Loki's actions come from severely damaged or lacking self-esteem.

He thought he was Odin's son and Thors brother, but never felt treated as Thor's equal despite his own recognized achievements (Hogun saying Loki is a masterful sorcerer when saying he could have brought the Jotun's into Asgard) and so acted out in a small way with only the intent of delaying Thor's kingship. When he incidentally figures out he's not Odin's son and is in fact a Jotun, worse, Laufey's son-- he verbally explodes because Odin had been lying to him his entire life and brought Loki up on those lies and half-truths. ("You were both born to be kings" "You'd never have a Frost Giant sitting on the throne of Asgard")

Loki's actions throughout all of Thor 1 are his attempt to prove himself a worthy son and he is repeatedly reiterating that.

What superiority he does feel for humanity for a time is quite literally a trait of all Asgardians, they all think they are above humans. Frigga is especially pissed at Odins choice of banishment when she finds out its Midgard, Loki compares them to ants (while again, mind controlled and exaggerated), Odin compares Jane to a goat in DW and gives Thor a mini lecture for him loving her. No one on Asgard respects humans, but if I'm going to take the Loki show in consideration then I can most certainly say Loki definitely does when he's around the long enough while still repeatedly assuring he is a god without deprecating them in the later season. Y'know, like Thor did after a while on Earth and interacting with the Avengers.

Craving admiration

This is something that fits Loki to a tee, I could not lie on that front. Loki, time and time again, does want admiration and even has a play produced (Though mentioning the people wanted to commemorate him) that highlights his sacrifice in DW and ends on that note since we don't see the play continue after Thor's actor mourns Loki and we get an Odin actor expressing love for a child actor portraying a Jotun Loki.

He definitely is a man that craves admiration and love, and the play doesn't help the case I'm making.

+1 point to Narcissistic Loki, need 4 more

Exploitative relationships (i.e., manipulation)

This is one of those criteria that seems obvious but, again, is not. Loki most definitely exploited Clint, Selvig, several SHEILD agents, and attempted to do so with Tony before throwing him out a window when it was obvious he would not be able to accurately manipulate them. But like with his grandiose nature, that was under the duress of Thanos and the influence of the Mind Stone. If Loki is not in his natural mental state, it cannot speak for his psyche in any meaningful way.

Outside The Avengers, Loki doesn’t show this trait either. Thor 1 only has him reiterating that Heimdall and the warriors, as citizens of Asgard, do have to listen to his rulings and descisions as current King of Asgard with Odin out of commission. Initially to continue Odin’s order of Thors banishment, then stressing it to deal with the war when Heimdall remarks he couldn’t see Loki. In Dark World, he’s the one being manipulated to help if that’s how we’re wording it when Thor recognizes he needs Loki’s aid and offers to let him get revenge for their mother’s death. Ragnarok continues to lack manipulation on Loki’s part, and the Loki Show has him again being manipulated for the benefit of hunting down his variant.

Little to no empathy

Very much not the case. Again, the interpretation is skewed by the fact he’s a god dealing in the world of mortals, but his actions with other Asgardians is enough to point out this just does not fit him. The moment he learns Frigga’s death he visibly becomes very depressed and trashes his cell, acting on Thor’s behalf with eagerness because he’s getting a chance to avenge his recently slain mother. He repeatedly endangers himself for Thor and Jane in the following fight scene, even taking on the same injury that killed his mother, but he survives. Before this, he’d almost gotten sucked into a black hole grenade protecting Jane.

In Thor 1, he acted continuously in the groups benefit by forewarning a guard to fetch Odin so they wouldn’t be in danger in the first place and when they inevitably did end up on Jotunheim continued to act defensively of the others in the fight. He didn’t want them hurt and called for Thor that they had to go once Fandral was stabbed repeatedly with ice spikes.

In Avengers, despite the Mind Stone, Loki did pause at the destruction of New York and cried when he actually hurt Thor. I say despite because it’s noted his anger and envy were heightened under Thanos’s control, feelings which mostly attest to Thor, but Loki still reacted that way.

In Ragnarok, Loki does visit Thor in his confinement and tries to talk to him about the now shared feelings of being lied to your whole life.

Loki is empathetic across the main MCU, there’s not really much ignoring that

Identity is easily disturbed (i.e., can’t handle criticism)

Definitely disturbed. Loki has a lot of issues with his identity and self-worth stemming from Thor 1 that, while not really picked up on in later installments, are the catalyst for most all his future actions.

To get into the specifics of this trait, Loki does "retreat from or deny realities that challenge grandiosity" in the fact that he does attempt to deny and destroy his connection to Jotunheim and Laufey in order to reaffirm his grand identity as Odin's son and a worthy Prince of Asgard-- by destroying Jotunheim and killing his biological father he is seriously trying to retreat from his reality by destroying the part of it that's threatening his identity.

+1 on Loki being a narcissist, 3 more to gain to be one

Lack of attachment and intimacy

Much as I don't like it and as much as I think Loki as he's depicted might have some other issue with intimacy, Loki is a well-connected person. He has obvious attachment with his parents, though Odin's becomes more strained, and had a good relationship with Thor. In the show, he does form genuine bonds with Mobius, Sylvie, and the TVA crew to the point of self-sacrifice so that, well on the larger scale the whole Multiverse acquires freedom, Loki does it because the alternative is killing Sylvie and his friends not being free.

Loki might be avoidant of attachment and the risks it brings, but he's not devoid of it for his fellow Asgardians or humans when he does form attachments to them.

Feelings of depression or emptiness when not validated

This again came with very skewed data but, alas, I will lean towards Loki having this trait. He visibly droops and loses energy when lacking in attention, perking up when the opportunity reappears before quickly taking it.

+1 point to narcissistic Loki, 2 left to get

A sense of entitlement

Skewed, heavily, but to reiterate Loki "I never wanted the throne, I only ever wanted to be your equal."

Loki, at the core of it, wants to be treated as Thors equal. Does he come off entitled? Yeah. But again, he's a prince. He has been raised as one for over 1,000 years, he's got much different standards than the normal human. Loki doesn't want to lose what friends, he wants to live a life that's not in his brother's shadow, he wants to be free. That's not so much entitlement once its boiled down as it is... decency.

Can feel like others are envious of them, or may envy others

He most certainly envies Thor; He's the golden son with seemingly everything, but Loki doesn't ever claim or act like a person to be envied. I'll give him a half point here

+1/2 to narcissistic Loki, leaving him at 3.5 points out of the needed 5 to be considered for NPD.

So yeah, I really don't think Loki is a narcissist and the DSM-5 seems to agree with me.