You've received lots of good info.
Once you rule out (hopefully) any sensory issues, then I agree with Marta W.
My nephew is autistic and only ate very starchy carbs like your nephew, about 10 items and thats it.
If your nephew does NOT have a medical reason, then get the parents a helpful book on nutrition for children. If she won't listen to you, maybe she will listen to an expert. The parents need to understand how bad this is for the boy's health.
Have the parents watch those shows by Jaime Oliver or see if he has a book out. He's the British guy who has that show "Food Revolution" where his goal is to get the bad food out of our kids schools.
My husband has hereditary cholesterol issues. Just had a quadruple bypass at the age of 39 (he is thin, otherwise very healthy). The cardiologist said this will become more and more common b/c of all the overweight children he sees and all the garbage they eat. Kids are getting physicals for high school and their cholesterol levels are terrible.
You are a good aunt for caring. Do what you can, I wouldn't want to see that boy having health issues b/c of something as controllable as a diet.