@bluejay
I agree with @swiley that the headline is ignoring the base rate, but the article makes a second, subtler error too.

It argues that, among those who get the Delta variant, vaccinated and unvaccinated, a higher percentage of those who are vaccinated die, making the same basic insinuation as in the headline. The error is that this ignores all the people who, thanks to the vaccines, didn't get Delta at all.

Suppose I create a miracle vaccine that prevents 100% of non-lethal cases and 95% of lethal cases. Now, in this hypothetical, there's a 100% death rate among breakthrough cases. This misleading result is an example of, I believe, Simpson's Paradox: https://plato.stanford.edu/entries/paradox-simpson/

Based on the article, the real percent death rate for breakthrough cases is 0.855% (402/47008), which is, misleadingly, several times higher than the 0.167% (253/151054) rate for unvaccinated cases. All this really shows is that the vaccines may be more effective at preventing less serious cases than at preventing deaths.