Except special relativity actually requires the true mass to increase when the speed increases. Mass/Energy is still conserved because energy is converted into mass (E=mc^2).
The effect described in the article is quantum mechanical in nature. In fact, the mass of the electrons is not changing. Only the "effective mass" is changing. Well, it turns out the effective mass is just an approximation we use to make the problem tractable. Basically, we look at the band structure in the material, and calculate an effective mass based on the curvature. If there is no curvature, such as in graphene, then there is no effective mass. However, the band structure for carbon nanotubes does have curvature, and therefor there is a finite effective mass. When the article talks about rolling graphene into nanotubes, they mean as a thought experiment. No one is actually sitting there with an atomic force microscope trying to roll a sheet of graphene into a carbon nanotube. So really, the paper brings nothing new. We already knew that there was zero effective mass in graphene, and finite effective mass in carbon nanotubes. Most likely, they are just suggesting a corollary to some other part of theoretical physics.