This is a fun piece... but what killed off the horses wasn't steady incremental progress in steam engine efficiency, it was the invention of the internal combustion engine.
Quite. For reference, the horse population of France didn't decline significantly until the late 1940's [0].
According to Wikipedia, the IC engine was invented around 1800 and only started to get somewhere in the late 1800s. Sounds like the story doesn’t change.
https://en.wikipedia.org/wiki/Internal_combustion_engine