There are some deadfall branches in there, and I think they hang some others in there too, but otherwise it is a small rocky cave. I believe there is a wire mesh ceiling open to the sky.
I know San Antonio is notorious for poor exhibits for larger mammals, but this appears nearly as bad. With no actual foliage and a bare, concrete floor this appears to be a very poor exhibit for such facinating creatures.
And yes Ituri, just finished reading about tree shrews, wanted to see how American zoos treated them. Looks like Woodland Park has the best (as far as I've seen).