Your son IS eating "healthy" to me. But per the title of your request... I guess you don't think so??
Ages and stages... throughout their years, they will go through certain food phases.
How about tofu? Or eggs? Stuffed deviled eggs? boiled eggs? poached eggs? scrambles eggs? My kids love these. My girl as well, goes through moments of not liking meat. I don't force her. She likes cheese and eggs. That's fine.
Or how about turkey? or Ham, or lamb, or BBQ meats? My kids like anything I BBQ on the grill.
Or how about nuts? That has protein in it.
Or, make smoothies for him.... add Pediasure to it, or peanut butter.
Your son does seem to eat a variety of things... but maybe just not what you wish him to eat. You are lucky he likes vegetable things.
Some people and kids, are just naturally prone toward more "whole" foods ie: vegetables, fresh things, fruits etc., and they don't like "meats." My son is like that. It's fine.
Your son seems to have a natural inborn propensity toward "healthy" foods. I would encourage him in that. When I was younger and a child, I was like that too. My Parents loved that I liked healthy un-processed foods and they didn't have to "teach" me to eat it or force me to eat it. My reason was, that processed foods and some meats, gave me a headache & stomach ache. My system was just so used to eating "clean"... that it upset my system if I was made to eat other things, which I did not care for. I just liked natural, whole foods and vegetables and fruits. It was just "my" taste and preferences in food. My sister on the other hand, only liked junk food and that was another story.
He's growing fine though, per the Pediatrician. I wouldn't worry. And he takes vitamins. Sounds fine to me.
Or, how about milk? Does he drink that?
All kids go through food phases. It passes, then another one will crop up. Then when they are teens other food issues comes up. So, pick your battles, and be careful not to turn it into a "control" issue. As an adult, I wouldn't want to be made to eat something I didn't want to myself. Kids are just picky sometimes... and as long as they are growing, healthy and developing normally... it's okay. Just my own feeling on it.
All the best,
Susan