From general systems biology perspective everything that moves body metabolism away from it's normal state for short time seems to give benefits, exercise, cold, heat, hunger, ... allostatic load that is not chronic is generally good.
They did say short time and non chronic. Is sleep deprivation really something one can experience in a short time? In my definition, doing something very difficult like lifting a heavy weight qualifies as extreme stress and would be beneficial; some other things would not. Maybe it would work better for you if they added the word "moderate" to their definition, but generally I would agree with their assessment.
My hot take hopeful guess is that heat shock causes upregulation of protein degradation / chaperone activity, thereby disrupting protein aggregation involved in AD, PD, et all. One can hope
From general systems biology perspective everything that moves body metabolism away from it's normal state for short time seems to give benefits, exercise, cold, heat, hunger, ... allostatic load that is not chronic is generally good.