When ants run in circles like that, it's called A death spiral/Ant mill. It happens when army ants can't find their way back home, and start releasing pheromones for help. They then accidentally run in a circle, which causes the more and more ants to run in circles. The ants eventually die from exhaustion.

The deer on the other hand run in spirals to confuse their predators, and increases the deer's chance of survival.