Can I use Google Cardboard with non-NFC phones?
NFC is used to auto-launch the application when inside a Google Cardboard device.

It's a way of the app to know that it is inside a cardboard device and it can launch the application in VR mode. When in VR mode, the display is split into two parts. 

So, in short you can directly launch the application normally and select the cardboard demo app and then insert it inside the device.