Check out Mark Sarnecki's theory books. He has one for each level of RCM theory; it literally runs through every theoretical concept just up until you would start four part writing. If you work through the books with him (if he's dedicated, he could probably do the first one in under a month), then he will get a good background with key signatures, chords, cadences, RHYTHM (which a lot of students lack), musical terms (french, italian, german, symbols), and basic analysis of a passage.
Also, he might be interested in four star books. They only really work if the student can remember to do a few a week, and I've found that any students under 10 forget every single week about the four star. Maybe a grade 4-5 four star book (which would have grade 2 excerpts a line or two long for sight reading) would be good, considering he's doing stuff from the grade 2 for sight reading. Ear tests are good too (4 star books have a section on these); identifying the quality of a chord, or repeating a rhythm or short passage really help develop ear. Combining that with the sight reading and drawing parallels will help him understand what a passage could sound like at sight before playing it.
Scales are really good to solidify his technique; be very specific with things like fingering and wrist rotation for the technique.
I actually have a student like this too; after the first lesson he found a few songs from Super Mario and learned them all! It was like he wouldn't stop practicing until he could play them; and again, these were much more advanced than what a 13 year old would play at a first lesson.
Maybe give him the url for this forum? I remember I found this place when I just started high school and had not heard of any of the stuff by many great composers. If he's really interested, he could spend hours looking through the threads for little bits of advice.