They have been issuing this diet for many, many years. From what you posted, it matches identically the diet I received in 1993. They wouldn't still be doing it if it doesn't work.
I too thought it was suspicious when I saw it; I mean, come on - vanilla ice cream and hot dogs? However, I can personally confirm that this diet does indeed work, as I was put on it in the last months of DEP before I went to boot camp, but it is intended for short-term, "emergency" weight loss. It's a chemical diet, meaning calories, carbs or protein aren't the important factors. It's the combination of the particular foods that helps to induce weight loss and acts as a cleanser.
This particular diet is meant for people that are joining the military but need to lose some weight to meet the BMI standards. I went on this diet for 2 months before joining the Navy. I have to say that it gets old and boring pretty quick, and I don't care for some of the items on the menu, but it does work. It helped me lose just enough weight to meet the Navy's regulations.
It is not really meant for the general population, because it is not the healthiest of diets, and is not intended for use over long periods. You will lose a lot of weight in a short period of time, which is why they generally only give this diet to people in DEP (Delayed Entry Program) who are not quite at the requirements, but who aren't losing the weight fast enough on their own.
If you are concerned about protein because you are building muscle, or already have built muscle, then you probably don't need to be on this diet anyway. This is for people that - to put it bluntly - are too fat for the military's standards, but not so fat that they don't think you can make it. I was in this category.
One thing not mentioned in the diet plan above is that you are also only supposed to drink water; optionally, you MAY drink tea or black coffee, but you should not use cream or sugar or any other additives because it can offset the chemical balance of the diet. Also, some seasonings are allowed, but try not to get too exotic. The more ingredients listed on the container, the more likely it can interfere with the chemical nature of the diet. I recommend just sticking with salt and pepper if you can. EDIT: Never mind - just noticed it said the same thing under the menu.
If it's not listed, it's not included. For example, Day 2's dinner of "2 hotdogs" is JUST the hot dogs - no buns, no ketchup or mustard, no relish, nothing else.
The "3 on/4 off" is specifically because this diet is NOT the healthiest diet. It does cause a lot of weight loss, and they don't want you taking it every day of the week. However, you shouldn't go back to a normal diet on the 4 days. You should still try to eat healthy, but you can splurge a lot more than the diet plan.
Dice up a skinless chicken breast in a salad tossed with your favorite kind of vinegar, olive oil, and seasonings. Have some fruit or yogurt (preferably organic, as it doesn't contain high fructose corn syrup, which you should avoid). Snack on vegetables. Just eat responsibly during the four days off, and you can avoid massive caloric fluctuations. But make sure you enjoy the food on the four days off, or you won't be able to stand the diet after the first couple of weeks.
Water is your BEST friend. You can lose weight just by ditching all other drinks for water. And drink lots, 5 or 6 bottles a day is a good goal, if you can't manage to drink more. The benefits to drinking lots of water are numerous.
Also, make sure you start exercising when on this diet to supplement the weight loss and increase your metabolism. This carries a benefit other than the obvious; it prepares you for boot camp. You don't need to do anything fancy, just push-ups, sit-ups and jogging (or start by fast walking). I don't know if the requirements have changed, but when I was in, you needed to be able to pump out 70 push-ups, 60 sit-ups, and run 1.5 miles in 12 minutes to pass the PRT at the end of boot camp. Nothing too tough, but if you can't do that right now, now is a good time to start working on it.
I can offer a couple of other tips to people that might be extremely close to the requirements, but not enough. The military measures your waist, neck, height and weight to determine your body fat index. Just before I was supposed to go into boot camp, I was still slightly over the requirement. My dad used to work in medicine, and remembered the silly fact that we shrink throughout the day, since the longer we are on our feet, the more compressed our spine becomes. This compression relaxes while we sleep, so we are technically at our tallest first thing in the morning, and I had been measured later in the afternoon, after either a day of school or working. We went back and had my height measured again as early as we could, and sure enough, it was just enough to put me BARELY within the requirements.
Also, you could go to an independent doctor and have a proper and more accurate BMI measurement done, such as by hydrodensitometry weighing or DEXA. If it says you are within the requirements even though the military says you aren't, the military doctors will usually accept it and give you a waiver; at least you could do this back when I joined. Note however that independent tests must be done at your own expense.