I recently bought the game while it was on sale and after downloading there seems to be no installer or start.sh. There is only a 'game' and 'support' folder. What do I do?

Are you sure your download was complete ?

The additional files are near the end of the archive, so if you've a partial download you'll not have them.

Here is the size and md5 of my archive :

(kilobug@aoskar) /home/share/gog/pillars_of_eternity $ l gog_pillars_of_eternity_1.5.0.7.tar.gz
-rw-r--r-- 1 kilobug kilobug 6973398349 Jun 22 19:02 gog_pillars_of_eternity_1.5.0.7.tar.gz
(kilobug@aoskar) /home/share/gog/pillars_of_eternity $ md5sum gog_pillars_of_eternity_1.5.0.7.tar.gz
c792b0e85f9cc753725b06d3edd8a836 gog_pillars_of_eternity_1.5.0.7.tar.gz