This list is very, very short.The basileos Alexandros IV of Makedonia was another foetus ruler (as long as he were a male).
There have been myriad additional child rulers like (in approximate chronological order):
Pharaoh Ahmose I
Pharaoh Amenhotep III
Pharaoh Thutmose III
King Labashi-Marduk of Babylon
Basileos Amyntas IV of Makedonia
Antioxos V Eupator of Syria
Ptolemaios XIII Theos Philopator of Egypt
Emperor VA Bassianus (aka Elagabalus)
Emperor MA Severus Alexander
Shah Shapur II
Emperor MOA Diadumenianus
Emperor Romulus Augustulus
Emperor Leo II
King Alaric II of the Visigoths
Shah Ardashir III
Emperor Alexios II Kommenos
King Baldwin V of Montferrat, of Jerusalem
King Edward VI Tudor of England
Tsar Peter II Romanov
Tsar Ivan VI Romanov
Also you have some of the titles wrong. The title of Shapur II and Ardashir III was Shahanshah, not Shah; King of Kings, not king.
Here is a link to a Wikipedia list of lists about child monarchs and rulers. Category:Child rulers - Wikipedia And probably none of the lists it links to are complete.