While this might not be the case in the Starter Set you are looking at, in the official rules (the full Player's Handbook), 1st-level wizards (PHB 114) are granted a spellbook containing 6 spells. They can then prepare a number of spells equal to their wizard level + Int modifier for casting (in this case, 4) using their two 1st-level spell slots.
At 1st level, you have a spellbook containing six 1st-level wizard
spells of your choice.
Spellcasting/Preparing and Casting Spells
You prepare the list of wizard spells that are available for you to
cast. To do so, choose a number of wizard spells from your spellbook
equal to your Intelligence modifier + your wizard level (minimum
of one spell).
Without viewing the source you are referring to, it seems that the 6 spells listed are their initial 6 spells in their spellbook, from which the player must prepare 4 spells each day to actually have available to cast. Detect magic, being a ritual spell, can still be prepared and cast as a standard action using one of the two spell slots, or it can cast as a ritual, in which case it does not need to be prepared and takes 10 additional minutes to cast.
In short, as far as I can determine, the character sheet is correct.