Hard No.

This isn't only unethical, it's also a really bad idea in practice.

Unethical: Every PhD position I have ever heard of requires you to do things that aren't part of the requirements to get a PhD (teach, do project work, help your supervisor with reviews, and so on). This is why you get a stipend or salary. Your prospective supervisor communicates very clearly what they expect from this position. It is not your place to decide that you would rather interpret the position differently. You are of course free to disagree with the assessment that this is important or fruitful, but then you need to raise your concerns equally clearly and upfront. Lying about it isn't ethical.

Really bad idea: You have been around this forum for a while. You must have noticed how all the truly terrible PhD experiences that people have start with a student having, for one reason or another, a bad personal relationship with their supervisor. Your prospective supervisor clearly feels very strongly about these videos, and most people care about not being lied to their face. If you now provide, in writing nonetheless, that you will help with these videos and then refuse to do so, you are running a serious risk of fundamentally breaking your personal relationship to the supervisor before it even gets a chance to develop. A few videos are surely not worth this risk.

If you decide to take this position, I suggest doing so with the mindset that you will in fact work on these videos. You don't need to be excited about it, and nobody can force you to do the best job in the world on them. Further, there is always a chance that your supervisor changes their mind on the subject, but I strongly suggest you don't take the position now with the full intend to weasel out of this task.

Compromise

You aren't interested in social media (albeit, you should perhaps give it a try) and you don't want to devote time to it, because it will detract from other activities, such as writing papers. But, social media is a formal requirement of supervision (in this instance). So, compromise:

Agree to participate in the production of social media videos, on the basis that you'll provide background material, be interviewed, etc., rather than the production aspects. Perhaps suggest that these aspects can be delegated to an undergraduate student (who could be paid), maybe a student in media.

Also, remember that dissemination is part of research, so perhaps also offer:

To keep an open mind and be willing to take a more active role in the future.

Thereby keeping your future options open.

Do not agree to something you won't do

This question is a classic loaded question. You obviously want to hear the answer that it is not okay for the student in the question you linked to to behave the way they did (and by extension that the supervisor who asked the question is right to be upset about it), so you have phrased the question in a way that makes that answer the only reasonable one. As a main example, you say:

I know I'm unlikely to enjoy doing these things as well, and would rather concentrate on my PhD.

This portrays the student as a spoiled and entitled student who only wants to do things they “enjoy” and think they can have the privilege of “concentrating” on their PhD. However, everybody agrees that PhD students sometimes need to do things they don’t enjoy, and that, unless they are self-funded, they may have to do things like teaching that prevent them from fully “concentrating” on their PhD. That is not at all what the debate in the question you linked to is about. I won’t rehash that whole debate, except to say that you completely ignore the significiant privacy issues (in fact you do not explain that the student will have to appear in a publicly available video with worldwide distribution), as well as the fact that it is the supervisor in that question who comes across as entitled and borderline-abusive in wanting to force their students to participate in activities that contribute nothing to their training or professional development in order to help the supervisor’s career.

In summary, this question is not at all the “reverse” of the question you linked to. It may be worth considering on its own merits, but I think it bears little connection to the situation described there. Also, while it’s possible that the student is behaving inappropriately, that would by no means imply that it is “okay” for the supervisor to act the way they do. Another way that your question is loaded is that it implicitly assumes the premise that the supervisor’s behavior is proper, whereas (as the voting on the question you linked to overwhelmingly suggests) it is not.

Yes. If there's one thing you learn about PI management in grad school, it's that 95% of them have the attention span of a chipmunk on methamphetamines. It's always best to just say yes to stuff (especially stuff unrelated to your work) and then only worry about it six months down the line if you're asked again and have to actually consider that it's a serious request which you are expected to fulfill. Then you are free to say no, explain why, and have the argument. Your prior agreement to an off-the-cuff request is not in any way binding (any more so than the PI's prior agreement to get around to reading your thesis proposal by Tuesday, which will never happen until the thing is actually due).

It's not just ethical, it's the established standard. I would expect all PIs to understand this, and I would severely judge any PI supervising students who did not.

Ethically its borderline if its okay to say yes and then TRY to get out of it, but you'd have to be prepared to face the possibility that you can't change their mind and in that case you'd (ethically) have to do the videos.

More honest would be to make your misgivings clear to the professor, and hope you can find a compromise. Is there any reason why you can't do the videos, other than you think its a waste of time you wouldn't enjoy? Perhaps you have problems with anxiety or public speaking that would make it difficult for you from a mental health perspective. If you have a good reason, discuss it with the professor.

To echo what @xLeitix there is much more to a PhD than just doing your research and writing your thesis, and you are not in a position to judge what the "requirements for a PhD" are, almost all PhD requirements say something about "demonstrating good scholarship" or acting in a way that "becomes a scholar", with the interpretation of that often left to the adviser or committee. For example, no where in the requirements for a PhD does it explicitly say that work must be well documented, data open access and code version controlled, but that is absolutely a requirement for working in my lab. Many people see public outreach as an integral part of what it means to be a good scholar. In fact out reach work is a condition of many grants, perhaps even one that might fund the PhD position you are discussing.

From an ethics standpoint, yes (but with caveats).

You have the premise:
The professor is asking me something unrelated to the work in order to give me the position.

If this is the case, surely it is ethical to answer with yes as it will not impact the job. I knew a superstar professor who firmly believed that scientists should never have relationships - in his interviews, he always asked "Do you want to marry at some point?" The whole faculty, of course, advised prospective students to answer with "no". This question is, in my opinion, not different then your question.

However, there are two things to consider:

(1) Probably you don't know if making videos is relevant to the position. This is very likely! So you cannot assume your premise and therefore, you would deceive the professor (in another answer, your unwillingness to make videos is described as "you are not suited for the position). In this case, a lie would be unethical.

(2) You would damage your relationship with the professor when they find out. This is very, very dangerous -- in Academia, you really need good connections, recommendation letters to survive. So from an interpersonal standpoint, it would not be okay to lie.
(For example, the superstar professor I mentioned before terminated his student's position immediately after for some bizarre reason he found out that the student was dating someone.)