There are only two reasons I would choose to use gamestop streaming.
#1 DLC is included in streamed games.
#2 Digital copies of games are streamed free with physical copies purchased.
Since I doubt they will offer either of these, my interest is in the low to non-existant range for this service. Since gamestop only sells one pc video game (WoW) then obviously they are catering to console gamers. If you want console gaming just pick up a game-fly membership.
This could be the worst thing that ever happen to gaming just like OnLive, you want to play handheld games buy a Handheld, want to play Consoles games by a Console same way for PC. What about Mobile what about it, let me know when there's ARM and x86 on the same die with integrated graphics and hybrid from say Nvidia's Tegra 2 plus Windows 7, 8, or 10 i don't care all of that in your hand and you got somethings.