The OP's goal is to lose weight. And the routine says:
"These are going to be fairly brief workouts in which you will follow the resistance training above with an HIIT cardio session like I describe in another article about high intensity interval training.
You should also do HIIT for day 3."
After this 30days he will have lost a good amount of his weight then can concentrate on gaining muscle if he chooses with a 5/3/1 or 5x5 program ect....
Not sure why you are not open to different training techniques based on goals of the user. When something that doesn't sound like the norm is ridiculed that always befuddles me.
My answer will remain the same; you should never neglect muscle groups. Any routine can be tailored for weight loss or gain provided you have an understanding on how it is mediated. I've said it once and i'll say it again, workouts alone will not dictate weight losses. They can improve lipolysis and so on but they are not the determining factor. Granted, maintaining weight while doing so much cardio will be hard given the intense nature of the program and therefore subsequently lead to weight loss but the overall concept behind it is flawed.
Say, for example, if workout A and workout B over the course of the week account for the same caloric expenditure, then they will both produce the same end result. Ergo, neither one is either a fat loss or muscle gain tailored program. That aspect is the sole determinant of how you plan eat.
But anyway, i've had enough of going round in circles; but I honestly hope that your time here will open you up to a world of proper programming which will only serve to enhance your overall performance and physique.
I'll leave you with this for food for thought; one member here, JudoJosh posted a study done on crossfit participants which showed that 1 in 5 ended up with some form of injury due to improper programming. We know though, that XFIT works WRT fat loss/weight loss because of the metabolic demands of the programs. People who undertake these programs are typically looking for fat loss/weight loss + overall muscular development and the programs seemingly fulfill their expecatations, however what these people do not know is that many of the movements require great technical ability (snatches, cleans, deads etc.) and as they lack the skill to perform these movements with perfect form, this subsequently leads to injury. They also lack progression, planal balance etc. So my point is, although the participants might end up with the result they wanted, they could be left with a whole host of issues (postural, torn rotators etc.). Just because its a plan that works WRT fatloss, doesn't mean they go about it the right way.
While your plan may only be for 30 days, often those that steer clear of leg days anyway might feel compelled to think that they can maintain this program, thus ending up with the Johnny Bravo syndrome. I'm not disrespecting your suggestion because it deviates from the norm, as I try alot of programs (usually 1 per year just for fun) that are not considered normal, i'm saying its not optimal or developed in a good way.
I'm always open to different approaches based on users goals, just not ones that neglect muscle groups.
For some odd reason, they author of that book assumes that 2 days of chest + back will not promote overtraining whilist assuming 1 HIIT session + a leg day will. Obviously that author has absolutely no clue on the stressors placed on the system during exercise. The squat and dealift are 2 of the best exercises you can do for your overall body composition. 
