You can play Riven on Linux with ScummVM.
Support for Riven is not yet official, you have to compile ScummVM yourself to activate it:

git clone git://github.com/scummvm/scummvm.git
cd scummvm
./configure --enable-all-engines
make

Then launch ScummVM and add Riven game: point to GOG Riven directory.
Now you can play Riven on Linux (and other OS/platforms supported by ScummVM).

Source: http://wiki.scummvm.org/index.php/Git