In addition to the points everyone else has brought up, it's important to note that you're sort of always tracking moving objects with your eyes.

If you're not resting on something, your head is basically never completely still. Try moving your head from side to side while staring at one word in this sentence - your eyes will reflexively rotate on their own to stay locked on.

This isn't completely the same. Your vestibular system senses your head's rotation, and your eyes reflexively move in response to that, so they have a little more information to work with here. But essentially, it's just kind of the nature of our eyes to lock onto persistent visual objects, whether your or the object are the ones that are moving.