xvart, they are definitely climbing plants, with vines that can quickly cover fences (or sometimes trees) if they are happy. I don't grow P. edulis now, but I used to have it trained on a fence. That's a good question as to whether they can be grown as a groundcover, and surprsingly, I've never heard of anyone trying it. Of course, a huge vine, unpruned, will kind of go everywhere, with parts trailing on the ground. I don't see why it couldn't do that in principle. Most people I know are trying to fit as many plants as they can in a small space, so "up" is a good option.
One thing to keep in mind for clmbing is that the tendrils need something of the appropriate size to grab and wrap around. Most wooden lattices won't work by themselves. Chain link fences are great, as are thick wire or twine that they can grab onto.