Louis II created the title King of Italy in 844, and the title was given to various members of the Frankish royal house until 950, when one Berengar of Ivrea claimed the title (and was excommunicated for this). At his capture by Otto I of the Holy Roman Empire in 962 the title King of Italy became a title which was automatically given to the Emperor, until 1806.
Therefore most Kings of the Germans were also Kings of Italy, as the Holy Roman Emperor was usually the same person as the King of the Germans.
The only other claimant to the title was Arduin, Margrave of Ivrea, who claimed the title in 1002, but he never gained any support. The Margravate was later dissolved, leaving no more claimants.
Since in CK there is no way to correctly model the confusing history of the HRE (if done right, it should be an elective title which would *usually* go to the King of the Germans, but the Emperor was not always the ruling King of the Germans), it is best to equate King of the Germans and Holy Roman Emperor.
So the title and setup are certainly historical.