This is cool! But the important question of what mantle convection, and therefore tectonics, looks like on a toroidal earth is not addressed... for the 'donut' earth where surface gravity varies by a factor of 3 on the surface, one could envision subductions systems, possibly double (two-slab) types, setting up at the northern and southern polar rings, while spreading systems would set up at the inner and outer equators. I have no idea what would happen to lighter, more differentiated arc rocks... would they gather in the middle of a two-sided subduction system, even though that is a gravitational high? Given the instability of these planets to perturbations, it's possible that sufficient redistribution of mass due to tectonics and crustal differentiation would be enough to rip them apart.
It seems more likely that subduction would happen at the inner equator, and spreading systems at the outer. This is addressed briefly in the article- when plates move around the torus, they must compress to fit into the smaller diameter of the inner equator, and stretch out when moving towards the larger outer equator.
Also, setting up a geodynamo would be tough...