x17n

When I play a graphically intense game on the m14x r2 via hdmi or the laptop monitor will the laptop automatically switch over to the gt 650m even though nvidia control panel says the hdmi port and laptop monitor are connected to the intel graphics card?

No, you need to assign the applications to a specific graphics card. It does not depend on how much intensity is being used, but which application is being used. You can manually configure such things in the Nvidia control panel if you prefer