It's definitely real wood. I had the right side trim piece on my steering wheel come off and glued it back on. Now the left piece is letting loose and will need attention soon. The back of the veneer is raw wood indeed.

Sort of a late reply, but here goes. The material is wood, and it is veneer, but it isn't natural wood veneer, that is, it isn't shaved off a log or off of a plank sawn from a log and then used in that form. If it is "Fineline" wood, as that in my X3 is, it is an "engineered wood" veneer. This is a product made from inexpensive wood veneers, usually out of poplar or obeche wood, raised on forestry plantations and then processed into sheets of veneer. Those veneers are dyed different colors and then cut and stacked in very highly regimented order, with colored resin layers between each sheet of veneer. The ordered stack is compressed into a block which can itself be molded and is then shaved on its bias forming a veneer of veneers, the pattern of which can be made to resemble rarer and more expensive woods (and even protected species not anymore obtainable) and which can be produced in a way that allows a specific wood grain pattern and color to be reliably and nearly exactly produced in nearly unlimited amounts, a useful quality for mass-produced items where consistency in appearance is desired. The BMW veneers appear to be heavily laminated in a clear polymer that protects the wood and provides a glossy and hard surface not normally associated with natural wood, more like a lacquer. The production of these engineered veneers is particularly common for the the commercial furniture industry.

It's most likely engineered veneer. Look up the words Alpi veneer on Google. They use it for the finish ply on drums too.

You say the trim is heavily laminated in a clear polymer that protects the wood and provides a glossy surface.

What is the best method and product to remove scratches that won't destroy the gloss surface?

You can pop the trim pieces out and use Scratch-X or similar. Even a light buffing compound will work. Just don't try to do it with the part in place unless you want the liquid seeping into the surrounding textured vinyl.