Chicken nuggets are primarily chicken muscle tissue, end of story.

Yes they can include mechanically separated chicken, which is basically a fancy name for saying they scraped all the meat off the bones. But that isn't "mostly skin and cartilage", it's meat. There may be trace amounts of cartilage and small amounts of skin in it, but they are nowhere near the main components.

If you're still not sure, just look at the protein content of chicken nuggets. The quantity of protein can only come from actual chicken muscle. Skin has little protein and cartilage has virtually none.

There are a lot of urban legends out there about what chicken nuggets are made of. But they're precisely that -- urban legends. They're false.