Fox does this in real life, too. There are bunnies in our yard a lot this time of year, he chases ’em off.
The game I tried to mimic the style of is the now-closed-down Dream of Mirror Online, we used to play a lot of it together. It was full of really vibrant color!
I only chase them because they have no natural fear of humans anymore. There must be balance.
Sometimes I just shoot NERF darts at them from the window. Hitting them seems to have little effect.