That thread is making the same distinction I am. Its semantics, but HIIT has taken on a more specific connotation with the prevalence of Tabata and other's research.
For maximal fat loss, you want to be doing short, anaerobic intervals.
That said, I am troubled by the implication that running 800 meters intervals would not be HIIT. Its is, if you are running intensely.
For reference,
here is a good article on Effects of High-Intensity Intermittent Training on Endurance Performance, discussing who longer intervals (2-5 minutes) are used to improve competetive performance in medium distance endurance athletes.
You can do all kinds of stuff for HIIT. Use a bike, an armed elliptical, or full body exercises like burpees or thrusters or
front squats.