Installed glxquake-bin and tried running it. There is the shareware Quake 1 .pak file in /usr/share/games/quake1/id1 but seems like glquake does not like it. There is no man page for glquake, glxquake or glxquake-bin, and the README file that comes with the package is just an announcement. There is no message after emerging glxquake-bin that would inform about the expected location of .pak files.
*** Bug 135065 has been marked as a duplicate of this bug. ***
Post install info had been added. Thanks for pointing out!