Lhough he won't starve to death or anything like that not eating enough consistently can have a detrimental effect on learning. If you are really worried about his health you could give him a children's multi vitamin.
My nephew has a sensory input syndrome and won't eat anything that touches, that anyone else has touched, isn't exactly the same brand as he is used to and lots of other little quirks. At my mums, which he has been visiting since birth, he eats chips and hard boiled eggs and has just started eating Pizza (cheese onl. He is 8 and the skinniest little thing you will see but he is also full of energy (and a daily vitamin tablet lol).
1. No snacks between meals
2. No fuss at meal times. This includes sitting still and not fidgeting and not disrupting the meal for everyone else.
3. No getting up from the table until everyone has finished
4. Helping set and clear the table.
5. If he doesn't eat what is on his plate then he doesn't have to but he gets no pudding, treats or snacks in its place (be strong and don't give in).
6. If he says he doesn't like something find out why. Then next time offer him something that has a similar taste, texture, colour or whatever it was he didn't like and see how he goes. It could be a fad or he may be starting to acquire his own tastes.
7. Don't pander to his likes and wants. He gets the same as everyone else but occasionally serve everyone something you know he likes. If budget or time allows each member of the household gets a choice now and then? That way he see some that everyone gets a turn and he is not being treated differently.
8. Whatever you do, STICK to it. He, like all children, need consistency and the only place they get that from is you (and school obviously lol)