Vaccines greatly reduce your chances of getting infected from a given exposure, but they don't reduce your chances to 0. The more times you are exposed, the more likely you are to eventually get infected.
I assume that workers at a major infectious diseases hospital during an infectious disease pandemic get exposed many more times than a typical member of the general population. (Worse...they are exposed to people who are sick enough to need hospitalization, which probably means that they are dealing with people with higher viral loads than the infected people the general population usually encounters).
This is not COVID specific. There are breakthrough infections for measles and polio, for instance. They are extremely rare in large part because most people are not repeatedly exposed to measles or polio. Measles is ridiculously contagious (9 out of 10 unvaccinated people will get it after just a short exposure to an infected person--R0 for measles is around 12-18), but two doses of measles vaccine are 97% effective so even with it being highly contagious the spread is slow enough in highly vaccinated populations to keep outbreaks small.
Polio's R0 is around 5-7. The first widespread vaccines for polio (the Salk vaccine and then a little later the Sabin vaccine) were around 90% effective. They reduced the number of cases per year in the US by 2 to 3 orders of magnitude within a few years of their introduction.
For comparison the delta variant of COVID has an R0 about the same as that of polio and the mRNA COVID vaccines are at least as effective as the Salk and Sabin polio vaccines were.