I recently did some small work to port our Hexen II project (http://uhexen2.sf.net) to Qnx. Now available in the files section of the SF repository https://sourceforge.net/projects/openqnx/) are binaries for software versions of HexenII (Hammer of Thyrion) and SDLQuake.
These binaries were made on Non-commercial edition, 6.2.1.
The current HoT (1.4.0) source code won't compile out of the box, but this should be changed in the next release - 1.4.1 - which may (;->) be out shortly. The SDLQuake binary is a fairly poor version of Quake, and mouse seems broken in fullscreen mode, but I compiled it to test the sound problems on some cards our project has. Sorry, but I have to say sound may not work on all systems. People are welcome to leave messages at the HoT forums. The games are statically linked with SDL-1.2.9. Thanks to Sam Lantinga for the SDL libraries. They're terrific.