You didn't even get the quote right. They say, "Vote at the ballot and vote with your wallet" (14:18).

That is, you use all the (nonviolent) measures available to in the modern societies in which the audience is likely to live.

You are asking people to do the same thing they are doing

you say, but people often don't vote, and people often don't select products based on impact on climate change, and Kurzgesagt is saying that doing this is your "tiny tiny part for the systemic change we need" (15:04).

And the reason they're a little vague about systemic change (though they do mention the major systems that need changing) is because of the quote you objected to about no system having proved itself capable of making the change. If you are trying to be neutral and evidence-based, what else can you do?

Nobody is completely neutral, and if I try really hard I can find minor improvements occasionally, but I think it's your ideology that is blinding you to just how close Kurzgesagt comes.