Indeed, when the first chapter is "General Unix and Advanced C", and the second one "Binary and Number Representation", that's a sign this isn't "bottom-up" at all. The list of topics seems reminiscent of the common CS textbook Computer Systems: A Programmer's Perspective.
That's fairly good. The sign of quality CS material requires explanations, analogies, summaries of facts, and diagrams. For example, explain pointers or C const rules to someone who only knows calculus. Most texts fail to accomplish these goals accessibly.
It maybe heresy to say, but Knuth doesn't explain concepts very well, reading more like a dense formal paper demanding a postgraduate mathematical background rather than elucidating concepts magnificently with both formal and informal terms. That's okay: subject matter experts need not be expert technical writers or lecturers. It could be the basis of another body of work by another author to write a compendium explaining and interpreting the Latin "Bible" to the masses. :)
I do think Knuth explains things very well. What possibly makes it difficult is he tries to keep it at a fundamental level rather than through the lens of any modern platform. One of the best chapters on random numbers is a good example. Beginner programmers might learn to import random (or secrets), lower level might learn to read from /dev/urandom and OS designers might ask a modern CPU directly. But that's not good enough. All of them depend on the fundamental concepts outlined by Knuth and do will any future computer.
Edit: yes, the chapter list is very similar to http://csapp.cs.cmu.edu/2e/samples.html with some OS topics thrown in.
For real bottom-up learning, Petzold's Code is one of the highly recommended books.