The second article (the source article) is poorly written. The author wrote a clickbait title, then buried the key argument several paragraphs in. The author should have realized that biased minds would misinterpret it (and worse, then use it as propaganda), so they did a real disservice to society. Here is the key paragraph where the author tries to right the ship:

However, the 20-fold decrease in risk afforded by the vaccine isn’t enough to offset the 32-fold increase in underlying risk of death of an 70-year-old over a 35-year-old. Given the same risk of infection, we would still expect to see more double-vaccinated 70-year-olds die from COVID than unvaccinated 35-year-olds.

The point the article is trying to make is simple: most elderly people got vaccinated in England (they had priority access). It is mostly younger people that haven't been vaccinated. So despite being vaccinated, more elderly people still die of covid in England than young people, even unvaccinated ones, because the elderly are more susceptible.

But there is another important factor, beyond the obvious, in this case:
this data is for England, where many of those vaccinated were not vaccinated with the most effective vaccines (Pfizer and Moderna), unlike in the US, so many of those vaccinated are more susceptible to breakthrough infections. And in the US, by contrast, the overwhelming number of recent deaths ARE coming from the unvaccinated population.

But here is the key takeaway I recommend for the future: don't just read a headline and think you've learned something new. Headlines are too short to give you enough context to properly understand most issues and they are mostly written to sound controversial, just to attract readership, which means they are often even further divorced from reality. You really have to read and digest the entire article to make sure you understand the information.