> That's far from a universal definition.

In sports medicine lactate threshold/anaerobic threshold/90(ish)% of VO2max has been the de facto definition for high intensity efforts for many many years.

You'll find plenty of examples on Google Scholar (including papers criticizing people for using these thresholds to define the intensity of workouts...)

> Running is generally considered a high intensity activity

Nope. Running can be a low, medium or high intensity activity depending on how hard you run (relative to your max).