Does "your hand closes over your fist below it" mean the hand is directly on top of the fist in the following definition for “hand over fist”? Thank you!
It does not mean that your hand literally closes over your fist, only that your hand is above your fist. This picture might help. The person's hand is closing above their already-closed fist.
I don't think that the definition you quoted is very well-written, because "your hand closes over your fist below it" is ambiguous, as you have found.
Imagine you're holding a rope tightly with one hand so it makes a fist. Now, imagine putting your other hand around the rope above your fist, but rather than closing your hand just on the rope, you close it around your fist. Now you've got your first hand just holding the rope, and your second hand partly holding the rope, but mostly wrapped around your first hand's fist.
Now, I have some experience with rope, and this to me seems like a pretty useless thing to do with rope, and you're far better off putting two fists entirely on the rope right next to each other -- watch any tug-of-war competition. That tells me either the writers there have made a writing mistake, or they don't know what they're talking about