No. One is a style of training and the other is a philosophy on training. They can co-exist but one can't replace the other.
You can do HIIT "intuitively" by only doing the sets that you "feel" is good enough. Though, that's what you should be doing anyway. If, for some awful reason, your HIIT program says to do 15 cycles, but you're about to fall down at cycle 9, then stop.
Alternatively, you can do "intuitive" training without doing HIIT at all, but you may not make as much progress towards the goal that HIIT is designed to achieve.
"Intuitive training" as they are describing it is just a philosophy that people usually call "listen to your body". Meaning, if your body is telling you you shouldn't do something, then don't.
If your program says you're supposed to do "x,y,z" today, but you're so exhausted that you can barely get out of bed, then don't do it. Wait till tomorrow.
If your program says you're supposed to run five miles, but your ankle hurts, then don't do it. Wait till tomorrow.
As far as weight loss is concerned, training "intuitively" could mean that you're moving less hence expending less energy. This merely means you have to eat less to make up for the lost expenditure. Although, in the long run, being "intuitive" would help prevent injuries which can slow down your progress even worse.
Being "intuitive" does not give you an excuse to not workout. Remember:
"Do not get angry at the progress you didn't make because of the work you didn't do." - Some quote I read long ago by somebody.
