This is an amazing published paper on the feasibility of a space elevator.
The big take-aways:
* Decreasing the x-sectional surface area by an exponential function as altitude decreases theoretically allows any material to be used, though the volumes required would be prohibitive for any but the strongest materials, and too steep an exponential function makes the geometries also not practically possible
* A yield strength of 46.5 GPa only requires a max-to-min cross-sectional area ratio ("taper ratio") of 10. A lower yield strength would require a larger taper ratio.
The material in this article has a yield strength of 9.6 GPa which is about 7.2% of the maximum strength of graphene and 20% of the way to 46.5 GPa, and I believe stronger than any bulk material previously manufactured. Reaching 46.5 GPa only requires 36% of the 130 GPa maximum strength of graphene, leaving lots of room for falling short on the actual average yield strength of manufactured product, and also including the required engineering safety factor in the design. And if we still fall short, we have some room to raise the taper ratio.
This TEDx video describes spinning carbon nanotubes to give them more than enough strength, which is basically what these people in this article have done! It also addressed the other concerns of the Gizmodo article. Since this manufacturing is firmly in the realm of engineering, now, I would expect to see a regular rate of increasing strengths in produced materials, as the processes improve. http://spaceref.com/space-elev...
TD;DR - Space elevator is entirely possible.