IMO it was a chilul Hashem, not that they owned a race horse or that it was run on Shabbos, but there was an idea that a Race horse can get a bracha for a donation
Why is it not a chillul Hashem to race a horse on Shabbos?
As silly as you make it sound, is it so terrible to ask for a brachah to succeed in one’s livelihood?
I think you define chillul Hashem not by what is actually a chillul shem shomayim, but rather, what makes you personally embarrassed in front of non Jews or non frum Jews.