I recommend going into the developer console and having a basic look at how they are doing it. From looking at the resources, you’ll first notice that it is driven by quite a lot of javascript :).
But the image resources are a little more telling - you can see that the background is really just composed of various background and foreground slices.
You could make such a background in a similar manner, and have two timelines in Hype that represent the x and y axis, and how they move in a parallax manner. While Hype doesn’t listen for mouse moved events, you could do this yourself and just drive the timelines. I’m pretty sure there’s some code on the forums that basically shows this if you search for “mouse moved” (A quick glance make it look like this result looks like what you’d want for one axis).