Do you really think that the people who worked on this study didn't consider your knee-jerk level-1 confounding factor? Obviously they look socioeconomic status into account when they were studying all-cause mortality, what study wouldn't?
The mechanism of action seems very plausible. Sauna's are moderate stress which spikes your heart rate temporarily (they say 100-150bpm in the study). So it's not surprising it could be protective for cardiovascular disease just like many other forms of moderate stress/exercise.
[1] https://jamanetwork.com/journals/jamainternalmedicine/fullar...