The "HIT" you describe is a very specific kind of HIT, in that they're specifically advocating one set of as many repetitions as you can stand:
Almost all high intensity training methods involve only performing one, all-out work set per exercise.
That's contrary to the sports science definition of intensity in the context of lifting, which I've usually seen construed to mean "percentage of 1RM". It's also not true of a variety of high-intensity training protocols, which use intervals or multiple sets to sustain high intensities of work output. Regardless, let's use Drew Baye's definition of HIT for the purposes of your question.
From the article you're using as a basis:
Bodybuilding or Strength Training?
High intensity training is not exclusively for bodybuilding or strength training or any one aspect of fitness. High intensity training may be used for a variety of exercise goals, by properly manipulating the relevant training variables. In addition to building muscular strength and size, high intensity training is highly effective for improving cardiovascular and metabolic conditioning along with numerous other measures of health and fitness.
The relevant training variables for focusing on strength rather than bodybuilding are the weight used and the number of repetitions. I am not convinced by the idea that time under tension or energy systems are the relevant variable instead of rep ranges. Controlling the rep range to focus purely on strength rather than metabolic conditioning, endurance, or hypertrophy just means that you should do all-out sets using weights or exercises for which you can only do five or fewer reps. I don't think that's going to be enough training stimulus with bodyweight work, even if you manage to find the exact exercise that is exactly hard enough without being too hard.
If you want to try this approach, I would first notice that nearly all the exercises in the recommended programs on Baye's site are weighted, not bodyweight. That's because a large number of bodyweight exercises make it difficult to get enough training stimulus for continued increases in strength and size with just one set. That said, one set to failure (while maintaining impeccable form) work strike me as sufficient and productive with deadlifts and pull-ups. I would be wary of this approach with one-arm chin-ups, handstand work, and one-arm push-ups. Those exercises involve some skill work and stabilization effort, which mean a significant degree of injury risk when doing sets to failure.