They do in my own personal definition :)

However, High Intensity Interval type of training aims to arrive at peak heart rate so it is an anaerobic exercise. The main indicators are "oxygen debt" (breathlessness), body temperature rise, profuse sweating, lactic acid buildup in the muscle (the "burn"), and peak heart rate maintained for 30 seconds followed by 90 seconds recovery period.
So it means SHORT intervals with high intense bursts of exercise, followed by recovery periods.