Good.
So my next step would be to make sure that the GP client is launched in 'Admin' mode and has the proper rights to install apps in the program folder on the local system.
For the sake of validation, can you just post the table line that contains your client update definition ? it should be something like :
GP2013R2 YE-update 2015 0 \\yourGPserver\GP_Ressources\Installation\GP2013\GP\ServicePacks\MicrosoftDynamicsGP12-KB3122624-ENU.msp MicrosoftDynamicsGP12-KB3122624-ENU.msp