I was not there, so I cannot say. Perhaps they had made arrangements prior to Shabbos for anything muksah to be handled by non-Jews. They definitely would have had to have lodging within walking distance to the track. They would have had to have non-Jews carry anything from their lodgings to the track, since you are not allowed to carry anything from one domain to another. I seriously doubt they would have been able to attend a Shacharis (morning) service It would have been quite challenging to figure out all the parameters and how to operate within them.
"...Churchill Downs, Kentucky is an unusual location for a Shabbos meal but the family celebrated in style. “We had a kosher caterer and lots of people at our table Friday night. Some of our guests were surprised. They said, ‘you guys really have Shabbos!’ Every hotel is very accommodating. The caterers are wonderful and do everything correctly with plastic utensils and servingware. It can be Shabbos wherever you are, ” she said..."
I can vouch for that. When I was younger, I would sometimes go to local national parks down south in the summer with a group of Orthodox friends, and spend Shabbos camping out. We made a campfire before sundown and cooked our Friday night meal, kept it warm until it was eagerly consumed by all. Saturday, we ate cold cuts and the rest of the fixings out of insulated ice chests. We brought our siddurim (prayer books) and davened (prayed) Shacharis without the customary leyning (reading) from the Torah, since we didn't have a scroll to bring with us, nor would we have risked harm to one bringing it out to the wilderness.
We also had to be careful not to walk more than a certain short distance and not to carry anything, since there was no eruv out there in the boonies. An eruv is a cordoned-off area (the strings are usually strung from telephone poles in the 'burbs and cities) area which is declared to be one single domain so that one can carry objects from one building to another and yet remain within a single domain. Without the eruv, you can't carry house keys, books, anything from one building to another. So yes, it's complicated to observe Shabbos outside of one's normal community, but it can be done completely within the bounds of halachah (Jewish law).