I think he had to go up the tree, he could go faster than the bobcat. I’m not sure how easily the bobcat could maneuver that high.
Cats are pretty agile. Here’s a leopard going after a monkey high in a tree: https://imgur.com/iKWmqFd
One morning, in the days before every person a videographer, our mystery cat was up in the walnut tree in the front yard. He was on a branch near the trunk about 10 ft up or so. A squirrel was below him wanting up. He eventually succeeded by racing past on the other side of the tree. Its tough when you don’t quite have the agility for the existing conditions. Some time later, maybe a year or two, I did see him feeding on a squirrel, so he had at least one successful hunt.
He was a mystery cat because we didn’t know where he came from and at the end we didn’t know where he went. He showed up in the high grass in the back yard, was hungry and stayed after we put out some cat food. He was an indoor/outdoor cat and disappeared one day. We suspected coyotes, but the new next door neighbor was suspect. He did not seem to like cats and may not have liked an animal roaming on his property.
The cat had a good life while he was here