Yes, you can build a set on location, but that doesn't mean that anything
built on location is automatically a set. A set is a setting
-- a place within which
the performances and action take place. It's the stage, essentially. The obelisk was at most a component of the "set" that also included the lakeside area, the trees, etc. (by the definition you quote above).
Okay, I did a little more digging, and I've found the answer. I was wondering if "set piece" could be the right term, but I didn't think that was the correct use since I'm more familiar with it in other senses. But the dictionary says
Theater . a piece of scenery used as part of a stage set, as a profile or three-dimensional construction built to stand independently on the stage floor
So that's our answer. If the location qualified as a set, then the obelisk was a set piece.