The purpose of this exercise
While serving as a bridge between the previous two exercises (where we have explicit vanishing points present on the page) and the next one (where you've got no vanishing points whatsoever), the rotated boxes exercise is also about learning to infer information about space and the arrangement of objects from neighbouring objects. Each box has others beside, above and below it, and by the time you're drawing one, some of these others have already been constructed. While their edges don't run perfectly parallel to one another, they do have a similar enough trajectory to some of the next box's edges to provide some important information.
While we do a lot of educated guesswork, our estimations of convergences and perspective in general are based on a number of more grounded sources. We're still aware of vanishing points, even if they're not drawn explicitly on the page or even present within the frame. They're still there, because we can see all these lines pointing so vehemently towards them. By not being so tightly tethered however, you're given a great deal more freedom to play inside of space, adhering to the spirit of the rules without being bogged down by them.
I think this is a critical part of drawing, and puts you in a much stronger position than someone who's only learned perspective through the laborious plotting of innumerable vanishing points, reference points, measuring points, and so on, and who goes on to draw a dog without understanding how perspective can apply to it. Perspective, form, 3D space - these are all factors in everything we draw in some way or another, and so we need to learn to approach it in a more everyday kind of fashion.