OP- some of these comments are wild, and say very much about the posters and very little about the likely success of your daughter in the world.
I could be reading about one of my daughters. She is exactly like this! If anything, she's even more extra and does chatter on 24/7 and can go through phases of slightly manic behaviour where she's super-exuberant, very upbeat and so on. She is chatty, sociable, extremely clever, throws in random stuff, definitely gives monologues to her friends on the way home, loves life, laughs a lot and is very kind to others. She has been diagnosed with dyslexia, but has chosen not to bother with an ADHD diagnosis, even though we all agree she has it in our ND family.
Unlike as suggested here- she's very popular. People are drawn to upbeat, happy people, especially other young people. They find being around interesting people interesting. She has more friends than she knows what to do with and gets overwhelmed sometimes by the amount of invites (as she's not good at knowing when to say no). She is constantly asked out. She is a high achiever and gets good grades when she puts her mind to it.
Are some people mildly pissed off by her- yes, most likely! Not everyone is everyone else's taste, and out in the world, there might be people who avoid her, although they will be outnumbered by the ones who like being around clever, interesting, exuberant, outgoing people like her who often have great social skills (being able to hold a conversation about pretty much anything age 16 is a social skill highly valued amonst teens). But, and this is the big BUT, in her home and her relationship with her dad, it is terrible that he is basically so grindingly negative about her.
He is giving a terrible message to her which is about unacceptance, about not loving her the way she is- we need our parent on our sides in life, even if the parents do find some behaviour annoying. He's not required to watch the videos, he could even say 'oh I'm not watching a silly video about pigeons' to her and in a kind warm loving parental relationship that would be fine. But that's not what they've got-he's constantly critical of her to you, and doesn't engage with her at all exept to try to put her down.
The example of Neurenberg- this is a major new film! Your daughter is more socially skilled than him in knowing this and talking about it in a nuanced way which is more in line with contemporary historians. He's the dick here,
Videos on the way home: that's how young people communicate with each other- I thought it weird at first, but they send tiny clips or voice notes to each other and then the others send tiny clips back, it's like slightly delayed communication. She's communicating with you all on the group chat including her siblings, she's highly engaged with you as a family, this is good news, not sign she's a narcissist! If you want to avoid, don't watch.
I would be taking him out for a coffee, say you've noticed this, and if he says basically yes, I don't like her, I find her annoying- I'd give him a true piece of my mind, it's not enough to be part of a family, he personally as the dad needs to find ways to show her that he cares, that he loves her and accepts her, otherwise all this subtle and not so subtle criticism of her vs the others will come home to roost and she will go off to university and avoid coming home to see that look of disapproval on his face. This is honestly a big deal- women with good relationships with their dad do better in life and in their own relationships, call him on this and ask him what he can do to improve it (and it's not watching pigeon videos). I won't have my own children devalued in my house.