1FEE 1993 value is obtained under the assumption that the positronium Rydberg constant is exactly half the hydrogen one.
2DOLGOV 2014 result is obtained under the assumption that any mass difference between electron and positron would lead to a non-zero photon mass. The PDG 2012 limit of $1 \times 10^{-18}$ eV on the photon mass is in turn used to derive the value quoted here.