That book has a completely different focus... breadth instead of understanding argumentation.
I agree that the Programmer's Introduction to Mathematics is more likely to contain useful content (instead of being about how to develop the ability to reason carefully). It also has a LOT more breadth than the OP.
The free part of Chapter 3 "On Pace and Patience" is a key very important attitude toward learning from this book (especially on your own). If you are thinking about studying from this book, make sure you philosophically agree.
I tried to copy and paste a paragraph here, but it looks like it has been ROT-13 encoded in the PDF (or something)!
> [...] mathematical culture requires being comfortable being almost continuously in a state of little to no understanding It's a humble life [...]