I think the PDF has a scrambled page order if one would want to print this as a pamphlet... Should be like this instead imho:
The layout is intentional and is refered to as a revers z-fold. It can still be printed out and folded, though in the revers direction of a z-fold.
Though, a trifold (which you are refering to) it usually thought of as the default, there are quite a few ways to fold a brochure. A revers z-fold has the benefit of reading more naturally when laid out flat. Which is great if it is being used on a computer and one of the reasons I chose that layout format.