those directions make it way more complicated and more seams than needed. You can do this in rows with squares with the only diagnals being on the ends of the rows. It's just "on point" which is really no big deal at all.
I often look at the picture and come up with an easy way to piece - this one is very easy if you turn it 45 deg and view it as rows going across -
You have a row of stripes and square in a square, and a row of crosswise strips and white squares - no diagonals in the field at all. Very simple to construct. Very easy to match up not like the pattern that has you matching up a lot of diagonals. The only drawback is you don't have 45 degree seams in you square in a square, but unless you are using striped fabric, you don't see it in the completed quilt.