From what I’ve learned trying (and failing) to create transitions like this, the best way to achieve what was created in the example link is to check the ‘stack all pages vertically’ option. Each one of the transitions on Amanda’s site is a separate page with their own animation. If you look at the address bar, it changes as you scroll.
As far as I’m aware, that is the best of achieving the horizontal scroll. Should help you if you’re building a single page site!