How does the Orxify app do what not even the official TOR client for Android can?
Orbot uses iptables to proxy all apps through Tor, which requires root access.

According to the description of Orxify it uses Android's native VPN mode to proxy all apps through Tor. 

Apps that use the built-in Android VPN interface do not require root access. This is the primary advantage of Orxify over Orbot.

On Android 4.0 and above apps can create a native VPN connection without root access to send and receive all network traffic. In this case the Orxify app creates a VPN connection to Tor and routes the internet traffic through the VPN. This can be identified by the key icon in the status bar.

I have not used or tested this app and this explanation is based solely on my knowledge of Tor, VPNs, and the Orxify app Play Store description.