If I look at it through the lens of the last 10-years of "science-based" strength/bodybuilding training, there's nothing surprising there.
# On rest intervals
His description is pretty spot on. The rest times mostly affect the amount of volume you can do (volume is generally defined as #reps x #sets, though I prefer #reps x #sets x weight).
That's actually something really useful to know because it allows you to get the required stimulus when you are in an inadequate situation.
For example, imagine someone generally trains their legs with barbell back squats and hacks squats. The weight would be fairly high for those lifts. But if you find yourself in a situation where you don't have access or can't use those lifts (injury), you can leverage the lower rest periods to hammer the shit out of your quads with leg extensions or lunges and get the stimulus you need.
It doesn't mean you should only do that though.
It's pretty well accepted that at some point movements become "stale": your body doesn't recover that well after performing the same movement for long periods (e.g. >6 months), so you need to rotate them out. Not because "the muscle got used to it", but because your joints are aching.
Again, understanding how to manipulate rest periods can aid in this rotation.
Another thing is time availability. Doing squats and resting 5 minutes might be fine for muscle growth, but you only have so much time you can spend at the gym. So you need to balance that out as well when you are training.
# On training frequency
Nothing to say there, targeting a muscle more than once a week is pretty much a given.
Even ignoring the need for frequent growth stimuli, you can reason about hitting the same body part multiple times a week this way: Say your chest max recoverable volume (MRV) is around 15 hard (0-3 reps from failure) sets a week.
If you only train chest once a week, how good can your chest session possibly be when you have to do so much work?
0-3 reps from failure is extremely hard. If you do 4 sets on the incline bench, 4 sets on the flat bench, you still got another 7 sets to go on other exercises. The accumulated fatigue throughout the session makes it highly unlikely you'll really be able to push your chest significantly for the remaining sets.
Why not split your training between 2 sessions? 8 sets on one day, and then another 7 sets later in the week.
You'll get much higher quality sessions like that because fatigue won't be crushing you.
# On training intensity / failure
Again, nothing revelatory there. It's well accepted that you want to train close to failure but not necessarily go to failure.
That's why auto-regulated training talks about 0-3 reps in reserve (RIR).
I've alluded to this in the previous section but I should make it clear: Every exercise you pick has a signal-to-fatigue ratio (referred to as SFR in the literature). Going to failure may be a good way to drive muscle growth, but it's extremely fatiguing. You can't possible survive a 5 week training block if you're going to failure in every single session and exercise.
Once you understand that and that multiple rep-ranges work, you can pair exercises that are high-signal and high-fatigue (e.g., barbell squats, deadlifts) with exercises that are high-signal and low fatigue (e.g., leg extensions, leg curls). If you're dieting down and are energy depleted, it would then make sense to avoid high-fatigue exercises like squats (or at least minimize the amount of volume dedicated to them).
A common approach is to increase closeness to failure as you progress through the training block, reserving failure or at least 0 reps in reserve to the last week of the cycle. After that you hop on a deload week and drop fatigue to start a new block.
You may also want to vary rep ranges and RIR targets because after a while training in the same ranges may get boring :)
# What I disagree with Menno
I don't agree with the part about getting a pump and soreness. I agree that their presence is NOT necessary to cause muscle growth, but in my experience (and other people in the industry like the folks at Revive Stronger and Renaissance periodization), pumps and soreness are good indicators that a training session was stimulative enough.