IMHO the surface of such a planet should be nothing more than molten lava, as the outer parts of the torus are probably going to rotate much slower than the inner parts (much like the rings of Saturn do). This would not allow for any solid crust to form.
I agree with srl: gravitation must get gradually closer to zero in the inner part, where the molten lava, not being pulled down by any gravity, continually explodes due to the pressure of the internal gases, forming a fuzzy ring of (cooling?) debris, a gradually spreading chaotic mix of rocks, the greater part going towards the torus' real centre of gravity, leaving underlying molten rock exposed to follow their fate later on - in short a crumbling effect that cannot be arrested. This rocky chaos may later start collapsing in the middle of the hole, forming the seed of the future planet.
BTW any large enough asteroid impact would also spell doom to the whole torus planet and either wreak havoc, rip it apart (in interesting ways, depending on location and direction of the impact) or cause the central "hole" to collapse sooner, finally reducing the planet into a more spherical shape - enter the Torusmageddon :)
A torus is not a hollow sphere. The OP's article stated that the computed surface of the torus was an equipotential surface, meaning that the apparent gravitational force (a combination of actual gravity and centrifugal force) at every point on that surface is straight down into the ground. OP even calculates the strength of the apparent gravity at every point on and around the torus. Assuming the planet started out in this toroidal shape, it would be stable since the net force at every location is "straight down", so there would not be anywhere where pieces would just fly off into space.
I agree with srl: gravitation must get gradually closer to zero in the inner part, where the molten lava, not being pulled down by any gravity, continually explodes due to the pressure of the internal gases, forming a fuzzy ring of (cooling?) debris, a gradually spreading chaotic mix of rocks, the greater part going towards the torus' real centre of gravity, leaving underlying molten rock exposed to follow their fate later on - in short a crumbling effect that cannot be arrested. This rocky chaos may later start collapsing in the middle of the hole, forming the seed of the future planet. BTW any large enough asteroid impact would also spell doom to the whole torus planet and either wreak havoc, rip it apart (in interesting ways, depending on location and direction of the impact) or cause the central "hole" to collapse sooner, finally reducing the planet into a more spherical shape - enter the Torusmageddon :)
Just my two cents.