The centre of mass energy is actually going from 8 to 13 TeV so it is not a doubling of the energy. However we are increasing the luminosity (number of protons in the beam) too so we will probably have at least twice the reach in energy that we did before. While the article makes it sound like something new looking for Supersymmetry (SUSY) is something we have been searching for since the start of the LHC.
SUSY is the leading candidate theory to explain why the higgs is so much lower in energy that the energy scale at which gravity becomes important: the Planck scale. While there are good arguments to suppose that SUSY is within range of the LHC energy I would put about as much store in a prediction of which SUSY particle will be discovered first as I would in a 14 day weather forecast: there is some science that goes into it but there are so many unknowns that the prediction is likely to be junk. Worse, while we can be pretty certain that there will be some sort of weather in 14 days there is no guarantee that there is a lightest SUSY particle: SUSY might not exist in nature although this itself would raise some interesting questions.