Axles

Let us remember that magnets have always two poles. In the levitating magnets (see before) the poles were placed on the upper and the lower part of the donut. In this toy, magnets have also a form of donuts, but their poles are different - on the outer and inner surface of the donut. In the base magnets in the form of short sticks are fixed, with their poles up and downwards. They repel the outer part of the donuts in the pen, so the whole pen is levitating.

The levitating pen can rotate, but differently than in levitron, their rotation is not essential for the stability. The configuration of the magnetic field is such that the pen is pushed up and also slightly against the barrier. This barrier gives the necessary stabilization, like the stick in the levitating magnets.
If moved slightly away from its stable equilibrium point, the pen oscillates up and down, right and left, like the levitron in the well of the magnetic potential.