I downloaded it using the link in this thread. Maybe you have a different version of Tyrquake than I do.
However the the screen is always panning to the left until I tap on the right joystick of the game pad. I was able to get 'Quake Shareware PAK 1.06' to load. Please tell me which Quake(s) you have, how many PAK's it has per ROM etc so I can attempt to replicate your success. However the Github distribution of Tyrquake for other platforms indicates it only supports Quake and Quake World which I do not have at this time. Several days ago I saw a post which stated this xbox emulator supports Quake 1, 2, 3, and 4. At this time I can not get the emulator to launch using the PK4 or PAK's i have, hence I do not have the opportunity to test the navigation buttons. Please note I have many quake games all of which have PK4's and PAK's in multiple directories, hence I have roms.