Nope, you don't need Geforce Now to play other games.
You can stream from Steam on your PC to your device, using 'Gamestream'. You can also buy/play Android games by downloading them from the google play store or from the Nvidia games app, and you can buy & stream games via Geforce Now.
IIRC any games you buy on Geforce Now, you are also emailed a Steam key for he game, i'm not sure if this works in reverse though