Hello:
There is a glaze over the entire piece. I am kind of out of my depth. I have seen some wood treated in this way that was referred to as "boxwood" or "elm." It is definitely varnished wood of some kind. Is it polychrome?
It was an emotional buy on my part.

Ok, that's a little helpful.
The scene seems fairly complete and I don't see any areas where this looks to have been broken off BUT I typically associate corbel fragments as having a 90-degree angle where they would have been tucked into. I don't see that here.
Polychrome is colorful paint or glaze - we often refer to a "polychromed" surface if we don't know exactly what the compound is (lacquer, shellac, ink, milkpaint to name a few, most of which are quite difficult to identify without microanalysis but we generalize based on tradition). I am guessing this was shellacked at a later date and is not the original surface. It's almost certainly late 19th century and would be carved from a fairly soft wood (elm is hard, boxwood is softer; sometimes these were carved from camphor or teak). Guessing that the brown stuff covering the back is a paper or fabric lining that has been pulled off?
If this were to go to auction, I would expect it to be catalogued as follows:

A Chinese carved softwood architectural fragment
late 19th Century
Profusely carved with figures, horses, birds and a temple in a landscape, on a later stand.
12 inches high, 17 inches wide 3 1/2 inches deep
CONDTION: with a later shellac / clear lacquer finish, on a later stand
PROVENANCE: acquired at an Orange County auction
$400-600*
*represents a fair-market value for auction purposes; retail or asking price may vary.