Are the TLS constructions they're using documented anywhere? Is this a combination of Ring-LWE and, say, ECC, in case there are as-yet-unknown implementation faults in Ring-LWE?
It is indeed a combination of R-LWE and ECC because it doesn't yet seem reasonable to depend on R-LWE alone. Not only because of the possibility of implementation faults in NewHope, but also because of the possibility of significant crypto-analytic advances against R-LWE, even with classical computers.