It sounds like you've never run one. World class athletes can run an entire marathon at a sub 5m mile pace. While they could run a single mile race in 4:05 or so, it's not even remotely a low intensity effort to run a 5 minute mile, even for the fittest people on the entire planet.
Unless you've put real effort into training, 60+ year-old competitive marathoners have done a 20 minute tempo run faster than you ever have... and repeated it 7 consecutive times without rest.
Marathons are high intensity and extended efforts.
>"The definition of high intensity training is literally anything above that (lactate) threshold."
That's far from a universal definition. The phrase "high intensity training" often refers to a type of strength training popularized by the founder of Nautilus that involved lifting until muscle failure. What you're describing specifically is called anaerobic training.
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).