I found the study that the article bases this on[1]. It doesn't make this claim and instead associates a higher mortality rate to sufferers of all mental disorders, 67% of which are deaths by natural causes. That these natural causes are directly associated with the mental disorder isn't even something the study says. Anxiety is just one of the many disorders analyzed.
This is similar to attributing a lower life expectancy to all people with endocrine diseases (e.g. diabetes) and later saying hyperthyroidism (another endocrine disease) is the sole cause of death in that group.
- [1]: https://jamanetwork.com/journals/jamapsychiatry/fullarticle/...
But, generally, I've seen mortality causes listed as something like (1) cardiovascular disease (2) cancers.
Googling directly for "where does anxiety rank as a cause of death" the answer is something like "it's rarely the proximate cause of daeth, but is associated with higher all-cause mortality"