Is the verb for this gesture "wave off?"

The example you show would be better called a dismissive wave or a dismissive wave off This citation favors the former merriam-webster

Definition of dismissive:

• serving to dismiss or reject someone or something : having or showing a disdainful attitude toward someone or something regarded as unworthy of serious attention.

• As in:

• He responded to the question with a dismissive wave.

A wave off is neutral in refusing help. A dismissive wave or even a dismissive wave off adds the pejorative sense.

No, I don't think it is.

My dad does that exact gesture a lot. It's not dismissing the other person. It's not dismissing what they're saying. Rather, it's acquiescing.

Dismissiveness is rejecting someone or something, essentially saying, "I'm no longer going to consider this or you. You can forget about me ever letting that stand. Now go away."

However, what that gesture is conveying is the opposite of dismissiveness because it's a reluctant agreement, not a rejection. It's saying, "Whatever. Go ahead. Now I'm done with this and you. So I'm going." That's why it's always accompanied by the person doing the gesture walking away or at least starting to walk away. Whomever is on the receiving end of that gesture isn't being dismissed nor is what they're saying, but instead, they themselves remain where they are and what they say is being allowed to stand.

The wave-off gesture refuses someone and at the same time implicitly tells them "you're dismissed," which is another way of saying "go away now," like in the military. There are two different versions of it:

1. The gesture where someone flicks the back of their hand at you, like they're shooing you away. That's dismissive. You reject the other person and reject what they're saying, so you keep your ground and give a dismissive wave of the hand that indicates that they are to leave you, which is the exact opposite of acquiescing and walking away yourself.

2. The gesture that looks exactly like waving goodbye, except that it's accompanied by a smile that is meant to appear fake and an obvious refusal to listen to anymore. In recent times, this gesture has often been accompanied by the words "Bye, Felicia!" to affirmatively dismiss someone from the one's presence.

Anyway, what you see there in that video clip, that's displeasure, frustration, frustration from having to acquiesce because of not being able to get the receiver of the gesture to back down, frustration from not being successful in dismissing that person or what they're saying.

Rejection and negation are basal concepts in communication theory. (Ref: Marshall MacCluhan, The Medium is the Message, 1968) To “wave off” indicates rejection and / or negation of a conveyed position, idea or comparative status. The subtext of this may be serious or it may be in jest, further subtexted by possible ironical or other nuanced intent. Nevertheless, the core dynamic is that of rejection, with the communication payload being understood by the context of the relationship between the communicating parties.