Think about it, they'll gladly crawl under blankets and such for extra warmth/comfort. They understand the basic idea that things that are like fabric keep you warmer.

I think them watching us is more about the entertaining motions we make more than any kind of confusion about what we're doing it.

Besides, I've had cats that would find a recently "shed" skin and drag it into their bed and curl up with it. Dogs too, but that's a different subject. That points to them knowing that the fabric is a separate thing from us. They don't typically go and drag snake skins over themselves to get extra insulation. Nor loose feathers.

But you're right, they'll treat clothes as being worthy of cleaning when on us, so I also doubt they fully understand exactly what the deal is. It's just that I doubt they think they're part of our body.