I watched their video about this and I don’t think it’s really that simple. Yes, approval voting means your first choice will never harm your second choice, but your 2nd choice can still absolutely harm your 1st choice. In a situation where there are 3 (or more) approximately tied candidates, voting for any candidate which is not your favorite is likely to harm your favorite’s chances.

Also, their example of a “spoiler” effect doesn’t really convince me. Sure, they negatively frame it by calling the winner party “bad”, but that candidate got more first round votes than the other candidates so it’s logical for it to have an advantage over a candidate who is mostly a second choice.

It doesn’t seem like a likely scenario either, it requires a scenario where voters who prefer candidate A want B as their second choice, but voters who want candidate B have no agreement with candidate A.