I think you are a little confused with the terminology here. So-called, High Intensity Interval Training (HIIT) is often used to drop bodyfat and involves some form of, what would usually be aerobic work, e.g. running, biking etc done in a high intensity fashion, i.e. incorporating sprints at intervals. The exercise therefore becomes somewhat anaerobic.
High Intensity Training (HIT) usually refers to the kind of resistance training popularised by Mike Mentzer in the late 70s and Arthur Jones and Casey Viator before that. HIT enthusiasts advocate very low sets per exercise and per bodypart, perhaps 3 exercises with one hard set of each for a certain muscle group. Naturally, one must work up to this one all out set which can lead to (justified IMHO) criticism of the HIT approach - surely the sets working up to the one all out set could be construed as part of a more multi set approach?
Anyway, I won't delve too deeply into the merits or otherwise of HIT except to say that it IS performed with muscle building in mind and is usually effective for a short period of time - perhaps as a way of busting through a plateau.
HIT - if performed as it should be - relies on going to failure on the all out working set, that is the nature of the method. Positive failure and often negative failure too.
There is nothing wrong with the routine you linked. Certainly for a beginner, and I would suggest an intermediate trainer too. A beginner could literally perform one set of each exercise as outlined. A good way to learn the exercises and become familiar with weight training generally. A slightly more advanced trainer should perform at least one warm up set (same reps will do) on most of those exercises. Certainly the squats, leg curls, shoulder presses, rows, bench presses tricep extensions and dips at least.
Unless you eat however, you won't grow no matter what routine you do. Sounds obvious but so many guys are lazy with their food intake. A naturally skinny guy needs to eat several times a day, each and every day. Not just a day here and there. Easier said than done.