I want to change fActorStrengthEncumbranceMult game setting with a script. But my script reads it as an unknown variable when trying to set it to a different value.

Is there a way to do it?

gamesettings arent globals or variables, you ahve to use a function to change them. Plus you need OBSE to change them in a script:

http://cs.elderscrolls.com/constwiki/index.php/SetNumericGameSetting