I see in log that game doesn't have permission create files in your profile folder which is usually here: c:\Users\username\Documents\Arma 3\
Could you try run Launcher as administrator?
You can try copy you folder files to another location (outside of C drive) and set patch to this profile via this parameter https://community.bistudio.com/wiki/-profiles. This is possible set in Launcher in advanced parameters or start Arma 3 game executable with parameters which you need.

Sadly, running the launcher as an administrator doesn't work, the game still crashes upon startup the same way

As for the second solution, I don't exactly know what you mean, iv'e copied all the folders from the files and pasted them elsewhere, unless you would also like me to copy the launcher to apply the parameter. Could you also specify which launch command you would like me to apply? im not exactly sure. (Unless you only mean -profiles in which case ima dumb head)