He makes a point of including all the newer features of C, including fixed-size integers, thread API, restrict qualifiers, and atomics, and dedicate a very significant part of the book to them. On top of that he gives many best-practice advice, that you could call "modern", as they are often violated in 20+ year old C code (and often by people who learned C in the 80's, in my experience).
I'm not exactly sure why it's "modern" C, but it is an introduction to C via establishing a somewhat rigorous and complete fundamental understanding of it.