I agree, your body isn't going to adapt unless you push it beyond its usual limits. But for someone just starting a routine like this, whose muscles and tendons aren't accustomed to push up's, pushing yourself enthusiastically hard in the very beginning is just going to cause a ton of soreness, possibly an injury, and a high chance of quitting the program at that point. As I also said, once you're accustomed to doing the push up's, you can start pushing yourself harder without risking as much soreness. At that point, going for the burn isn't going to make you so sore the next day that you're going to quit the program.

Your point about strength versus endurance is well taken, but again, for someone just starting on the program who isn't already doing any strength training, they will be building strength in the beginning. Only after they reach a certain number of reps does this program really turn primarily into a muscular endurance program. Of course, at that point, you can just start piling the cats onto your shoulders while you do the push up's (Don't laugh, I've seen some pretty heavy cats over the years! )