Hey!
I've managed to fix it.
Simply, make a backup of these 4 files (GTAVLauncher, PlayGTAV, GTA5, and GTAVLanguageSelect), verify your game files via Steam (so it installs the new version), and replace the new ones with the backup files. The verifier had to update about 50 files, so there is probably something that the launcher is looking for.
For me, it works perfectly.