Intuitively, just imagine picking a starting point on each of the circle and the knot. Now walk at different speeds such that you get back to the starting point at the same time.

In fact, that's what the knot is: a continuous, bijective mapping from the circle to the image of the mapping, i.e., the knot. (As the linked answer says.)

Edit: I see now that the article already has this intuitive explanation but with ants.

Somewhat counterintuitively, all knots are homeomorphic to each other.