Basically it comes to coding and capability. 64-bit systems are able to use more RAM and use it better due to the release of archaic coding limitations. The bandwidth for memory use is doubled, thereby making it more efficient.
Historically, 32-bit systems were limited to 3GB of RAM. There were little tricks to allow 4GB, but it was never guaranteed to be stable and only programs written for it would be able to use it.
As for the G2A, I've heard many stern warnings about authenticity of Windows keys there. Use caution. The only true keys are the expensive ones, unfortunately. I've gotten games there, but a few bucks loss won't kill me. Losing OS support... that's another issue.