You’ll need to get Google Play Store on your Kindle in order to download apps and games like you would on a normal Android device.
Use Kindle Without Registering Account
For newer versions of the Kindle, you’ll be forced to connect to WIFI but if you select the ‘x’ button on the connect to WIFI screen, you’ll be presented with the Set up later option once you’ve closed this screen. If you have a new Kindle Fire, this will let you use your Kindle without having to register.