Calcium (most likely from dairy) is even more important for bone growth, the single most important requirement for height.
You're right about the calcium. My vegetarian son is now 17 1/2, still on the exact same growth schedule I followed (he's now 6' 1 1/2", as I was at that age, and I ended up 6' 2 1/4"), because he consumes plenty of milk and cheese. He gets no meat, not many eggs, and doesn't eat particularly high-protein vegetables. He's a foot taller than his mother, so he must have avoided all of her "short genes".
It probably has helped his muscular and skeletal development that he's been carrying a 30-pound backpack around school for several years; he never uses his locker but just carries all his books around because the school is huge and classes are far apart.