The book description had this sentence:
Discover even more great reasons to love knitting--circular needles make it so easy.
That suggests circular needles.
Working on two circular needles is one of the methods for doing small diameter circular knitting. As others have said even if the pattern says to do that you don't have to, double points or Magic Loop will also work.
On why they say to use 2 different lengths... there is no real reason for them to be different lengths but when I use 2 circulars I like to be able to distinguish the needles from each other. That is because you always want to work the stitches on one circular with that same circular and the stitches on the second needle with that needle. I happen to have some old nylon circulars that came in different colors and often use one white and one blue or something like that, but 2 different lengths would also be a way to keep track of which is which and maybe that is why they say that. They can be identical but you must pay attention so that you always keep the 2 groups of stitches to their respective needles.