Scrolling comes from the page moving in its viewport - it can be triggered by touch actions or mousewheel events. Swiping can be triggered by two events also: on desktop it would be a mouse down, mouse move, and then mouse up, whereas on mobile it would be a touch start, touch move, and touch end event. As the touch overlaps between a scroll and a swipe on mobile, that does make a small complication in how you want to handle it.
It looks like that page uses the fullpage plugin; taking a glance at its code it both uses scroll events and touch events.
Our older parallax example uses scroll events, but doesn’t do anything for touch so doesn’t appear to work correctly on mobile. It may be a good starting point though.