Arguably. Youtube is a video hosting site, it's not a political platform and has no obligation to host content it doesn't deem suitable for their platform.
Those videos should be sent to news agencies, (inter)national archives, the UN, war crime tribunals, etc instead (or in addition to) "entertainment" video hosting sites.
By parallel, misprision of felony is a crime in the US:
> Whoever, having knowledge of the actual commission of a felony cognizable by a court of the United States, conceals and does not as soon as possible make known the same to some judge or other person in civil or military authority under the United States, shall be fined under this title or imprisoned not more than three years, or both.
There is a moral imperative created when someone else is giving you these records. It's like someone asking you to call 911. You don't have to go out looking for emergencies to call 911 about, but you do have to deal with it when one is dropped in your lap. In this case "dealing with it" just means retaining a copy and making it available on some terms.
One implies the other. If your media backup and recovery plan is Youtube, then you need another plan.
For "not a political platform," Youtube has quite a lot of political content, and it's not at all clear to me why someone would think that the idea of a general interest video hosting site and a political platform are somehow exclusive at all.
And as far as obligations go... I'd imagine that there's no legal obligation, and maybe there shouldn't be, but that isn't the end of the question. As far as I know, I'd have no formal obligation to stop and render aid or even contact emergency services if I came across someone unconscious and bleeding on the sidewalk near my house, but that doesn't mean I might not be under some obligation.
And one problem is that organizations like Youtube often don't put themselves together in such a way that there's anyone interested in and capable of responding to these questions.
It's almost like they come across a turtle in the desert, and it's flipped over on its back, belly baking in the hot sun, beating its legs trying to turn itself over. But it can't. Not with out their help. But they're not helping. Why is that?
A general interest here seems commercial in nature and is thus susceptible to whims of the owner(s) and their ToS.
One possible solution seems to be something like a Wikipedia for videos, a non-profit org, but the cost of video hosting seems to still be prohibitively high for a non-commercial entity in 2018.
In the spur of the moment, in particular in a warzone, the proper place to store something is the last thing on one's mind.
Regarding "has no obligation to host content it doesn't deem suitable": Yes, sadly, this is a problem not unique to YouTube. All hosters get to decide what to host and to change that decision at any time.
Some people choose to respond to hosting on sufferance by becoming sycophants (placate the hoster with speech one believes won't offend the censors) but that is ultimately detrimental to one's own message and free speech overall. We have no solution for this that is really easy for nontechnical computer users because we all depend on other parties for Internet access. If homes had Internet access that could not be taken away, we might be able to recommend self-hosting. For now, in the age of the ISPs, the best we can do is massively decentralized hosting which uses no DRM, running additional nonfree code (such as YouTube's DRM in JS), and somehow getting a lot of peers with lots of storage and bandwidth to keep available copies of everything uploaded (we ought not decide that one message is worth sharing and not another message because that is the very problem we're trying to solve).
This is a tough problem to solve. I don't know what a viable solution will look like quite yet. But I know what to avoid: we won't solve this problem by placating big business desires for more control over what we say and how we get copies of other people's works.