APK stands for Android Package Kit — the file format used to install apps on the Android operating system. Apps downloaded from the Google Play Store are also installed as APKs on your device; the process just happens in the background.
six6's Android app is available as an APK file through official channels. Once installed, you can open six6 directly from your phone's home screen — no need to open a browser. You can find more details on the six6 app page.
Because APK files are installed directly, Android may show a security warning — this is normal. It is fine to allow the installation only for the official APK.