Let me start by saying that I have no knowledge of Linux OS.
The options on other OS's are:
1) Apple's Network MIDI API, and a compatible driver can be found for Windows. Not sure if there is a similar Linux one.
2) PureData/OSC. There is a Puredata script available from the app that you can load up into PureData on a Mac/Windows and PianistPro communicates with that. Prior to CoreMidi on iOS (ie. Network MIDI), this was the only way to perform wireless MIDI. I believe there is a Linux build of PureData. It is a bit fiddly to set up, and I can't provide much tech support there.
3) A wired connection. Buy a MIDI interface for your PC that works with Linux. Originally these used the Apple Camera Connection Kit to plug a USB lead into the iPad. (Note you cannot just plug a USB from iPad to PC - there has to be a MIDI interface in there somewhere) Then MIDI Mobilizer was released that did the same thing without the CCK, and output to two MIDI cables (so you'd still need a PC MIDI interface). These days there are a lot of iPad wired MIDI interfaces for you to choose from. The wired connection is less convenient but will have better latency and be more robust than a wireless one. All wireless MIDI communication can drop packets and occasionally leave notes hanging.