This is my understanding of it:
Some of the places are buffets, and while some do have a specific "kid's section" your kid can pretty much eat what they want. Well, pretty much, but for most children, they'll pick a hot dog over steak anyway, the restaurant might balk at your 6-year-old in the steak line at the buffet but probably your kid isn't going to go there in the first place.
For the non-buffets, here's the bottom line. It's Disney, and they love your money. If you are on dining plan and paid adult price for your 10-year-old-- if you've basically "paid" for a steak dinner and your kid wants chicken nuggets-- Disney will be more than happy to do that.

Chicken nuggets are quite a bit cheaper than steak.
We have a 10-year-old too and I balked at paying adult price for him. However, since we first started planning, he's shot up 3 or 4 inches-- the beginning of that whole puberty thing and I'm freaking-- and by the end of May he very well could be eating us out of house and home. But he's not very adventurous with food, not yet anyway.