The install definition file for Player Achievements did not contain a correct installation class
Looking at the detailed error, it told me that it couldn't access the addon's inc/install.def.php file. Yet the regular Linux permissions all looked identical to those of working addons.
Then I remembered that I use SELinux in enforcing mode on a CentOS 5 system.
First I used "ls -Z" on a working addon to see what attributes the files there had. It turned out that the info addon had "user_u:object_r:httpd_sys_content_t" as the attribute on all files and directories. So then I used "chcon -R user_u:object_r:httpd_sys_content_t ." from the new addon's directory to apply that attribute to all of its files. That fixed it!