COVID is airborne. It can move through the air, remain in spaces for a long time, and generally transmit much easier through the air than most realize. People don’t need to be in real close proximity to the deer to get infected, just close enough to share some air. With lots of people, lots of deer, and lots of COVID, there’s lots of opportunities for cross infection.
They compared the genetic sequences of the collected deer samples to available human ones and found 3 that were nearly identical, which suggests direct spread. From the article: