This is the bottom of it and a close up showing the little stumped legs. it stretchs out to a a 1 ft height when expanded 70cm long. and has no holding arms to attach to the top of the stairs. It could certainly be used as an expandable rack to put hot dishes on or sauce pans. My dad seems to think this is what it is.
I'd guess it's an expandable trivet to put hot pans and platters on. It could also be a cooling rack for pans out of the oven. If it isn't, it could be used as one.