First it should be said that the counter-claim made in the question that "[n]either charter seems consistent with killing or displacing all people in Israel, which would include Palestinians and non-Jewish immigrants", is very debatable. I will not get into a detailed analysis but I think the Wikipedia article leaves this very much in doubt. One could cherry-pick details to support this interpretation, or do the same to support the complete opposite. I will put this question aside.
As for the primary claim attributed to Yaari, it is notable that according to The Times of Israel, the Hamas-affiliated Shebab outlet reported that Sinwar stated months after adoption of current 2017 Hamas charter:
Over is the time Hamas spent discussing recognizing Israel. Now Hamas will discuss when we will wipe out Israel
Shebab's website appears to be offline at the moment, but I can see via Internet Archive that it is in Arabic. I hope maybe at some point someone proficient in Arabic can confirm the original quote.
Assuming the translation quoted above is accurate, it is not reasonable to interpret this as evidence of what Yaari said. However, there remains at least some room for debate here. The language of "wiping" Israel away has a complex history with respect to Iran, a major sponsor of Hamas. Iran has claimed that wiping Israel off the map means "the defeat of Zionist ideology and the dissolution of Israel through a 'popular referendum.'" Of course, supporters of Israel will say this is patently absurd.
In conclusion, I think we have no firm conclusion, because Hamas is ambiguous in its statements. I say this with the important caveat that an Arabic speaker might debunk the key statement that seems to support Yaari's claim. In that case, I would say Yaari's claim is an overstatement of the facts, but the question's own claims about the meaning of the Hamas charter remains a separate question.