If I were u I would find another tutorial. The fabric on the one you site is so busy I can't see what the demo is doing.
The busy fabric makes it confusing for me. I imagine she suggests cutting the fabric down the fold is for convenience and ease of cutting. However, that would depend on the size of your squares. I would not do it as it may waste fabric. I didn't read all the instructions but that suggests her squares are about 11" or so = the size so you can get 2 across the 1/2 width of the fabric. But find another tutorial.