Here comes the hard part.
There is an induced current in a closed conducting loop if and only if the magnetic flux through the loop is changing. The direction of the induced current is such that the induced magnetic field opposes the change in flux.
When you rotate the ball perpendicular to its magnetic axis, you make a change in its magnetic flux (ΦB), so the right part of the equation becomes non-zero. This induces a voltage (so-called electromotive force, ε) in the body of Spin Flux and since it's made of a conductive metal, electric current starts to flow.
Since the inside of the torus is solid, the exact amplitude and direction of the current are difficult to specify, but according to Lenz's law, one property can be said for sure: these currents will flow in a way that the magnetic field they generate will oppose the mechanical rotation of the magnet ball. You feel it as a smooth magnetic braking force that makes Spin Flux an enjoyable item to fidget with.