Well they got the holder of the tittle atleast right , sort of , according to wiki it was House of Zähringen Berthold II (1061–1077) . In the game it is Berthold I (1066)

Since the game is not that long out and the amount of historical info they had to work with is just insane its not a big deal . Someone will fix it eventually . However that they messed up a Duchys COA is suprising me

but nvm , this is about the first potential King of Slovakia  :D 

And Carinthia as the rest of Europe will fall under my great conquerors rule eventually  * evil-laugh-smiley*

However if we are 100% historicaly correct then there wouldnt be any Carinthian Coat of Arms until 1246. But fake substitute is gay. ;D Basicaly countries didnt have Coat of Arms until around 13th – 14th century before that only dynastical Coat of Arms were used. So for example Czechia used Přemyslid Coat of Arms. Carinthia had so many free lords in this time you are playing that we cannot say it was very unified state so there were many Coat of Arms used. Coat of Arms used in Carinthia depended on which lord was crowned by peasants. In 1246 Coat of Arms of Carinthia became stable and it was the one i showed before.