Copy the directory then run the launcher. It should set everything up correctly for him
Well correct me if I am wrong, but as far as I know OpenAL is not included in the Freespace2 root directory, so simply copying the game root directory onto other computer doesn't guarantee that it'll work right away; if OpenAL is not installed, it must be installed.
Otherwise yes, Freespace 2 Open works simply from a root game directory containing the game data and executables, and mods in appropriate sub-folders if they are present, and the necessary registry entries are created as the game is used... so "installation procedure" in ideal conditions mainly involves Copy-Paste operation and OpenAl check/installation if necessary. Upgrading the game to latest goodies is what causes the most part of confusion, if any.