SOLVED!
After a while I noticed that the above mentioned "dbghelp.dll" does not belong to Avast, as I got the impression of - it belongs to the game (C&C Generals ZH). That changes a few things. After a quick search on the web I found an issue regarding DirectX and this game, with a possible solution to delete this dll (the one in the game folder, mind - NOT the one you find in windows' system32 folder
) This solution worked for me.
Even though the original error message heavily pointet towards Avast, it was actualy the "dbghelp.dll" in the game folder that caused this error message
Final scores: AVAST 1 - EA Games 0. Let's send the guys over at EA a cactus for framing Avast!