I can tell you what's likely going on; check to make sure that your nVidia Control Panel has the .exe listed in it, otherwise it's probably trying to use the Intel chip, which is woefully underpowered. Right click on the nVidia Control Panel, then go to "Manage 3D Settings" then click the Program Settings tab. Navigate to the .EXE, select it, and you should be set.
That said, even if you CAN run Skyrim/Fallout 4 on a 650m you likely shouldn't. I had the M17x prior to my current machine, and found that even on Med., Dragon Age Inquisition would make it chug. Some Unity games also made it cry. As they get more "shiny" the 650m will be unable to play.
