(BTW, WJIII is actually outdated. The current version is the IV.)
WJ is a norm-referenced, individually-administered achievement test, whose best scores are age-based percentiles or other transformations of z scores. Grade-based normative scores are also appropriate for some situations. It is possible to report age and grade equivalents, but those are not generally recommended. (This does not stop institutions from using them for various high-stakes purposes, of course.) It does produce different composites for oral language, reading, written language, and mathematics, and has options for academic knowledge, which would include a little science.
In section V, the WJ is scored using grade norms, by selecting the grade to be entered (in this case, kindergarten), and then entering the resulting percentiles into the IAS.
In section VI, the WJ is scored using age, or using current grade (in this case, age 4), and the resulting percentiles entered.
With regard to the categories, one would legitimately be able to record scores for V: Language, Math, Reading, and VI: Vocabulary, Total Reading, Total Math, Total (Written) Language.
While his belief that he was not allowed to do subtraction undoubtedly lowered his math calculation score a little bit, if he is actually able to do subtraction, it's probably not a huge deal, as very little calculation skill is expected for children his age, so the age-norm-referenced scores would still be high if he did all of the addition. Writing is another issue, but again, these are age-normed scores, and few children his age have mastered handwriting. He's only being compared to other age-mates.
