After some poking around, I found this guide, most of which did nothing but the last few commands
triggered installing some missing items
and now the game runs. I don't know which of these actually fixed it.
This is a pretty awful user experience. There was no indication what was failing or what was needed. Steam's site has no documentation that I can find on getting things working well on Linux and most of the guides I found were telling me to install packages that I already had.