When you launch GG while connected to the internet, the Steam client will automatically check for updates and apply them before launching GG. It will tell you if it's applying them.
MAME Cab PC: i7 4770@3.4Ghz (passmark 9945), 12GB RAM, Win 8.1/64, GeForce GTX645 (passmark 1898); Shiny new laptop: i7 4800MQ@2.7Ghz (passmark 8586), 16GB RAM, Win 8.1/64, GeForce GTX870M (passmark 3598); Old laptop: i5@2.3Ghz, 8GB RAM, Win 7/64, Intel 3000 graphics