Wanderon: I had a different issue with 2.02.
Pillars of Eternity patch log
File not found (for patching): C:\GOG Games\Pillars of Eternity\PillarsOfEternity_Data\assetbundles\prefabs\objectbundle\draining.unity3d
Game shows proper version numbers - played through Temple of Ethos and got Gauns Pledge Flail with draining intact but after save/reload it disappears.
If you download it using the Gog Downloader AND you has the White march, try to download manually the Patch FOR THE WHITE MARCH.
Strangely, in the Gog downloader's links webpage is not listed but in the normal page it's does.
I had a similar error message, and after downloading manually the (even bigger) patch, was able to install it and just played some minutes in the White March without problem