my iPod slipped off my wrist and landed on the floor.
That is certainly an accident, and the warranty on the iPod does not cover such damage. That the loop slipped off your wrist does not constitute a failure of the product's materials nor construction. I don't know of any such strap where the manufacture guarantees that it won't slip off your wrist and hence would cover any such damage under warranty.
Sorry, but you will have to pay the replacement fee.
Bring it in to your Apple store and explain to them what happened and that Apple provided the loop for security. Perhaps in their discretion, they will exhange it for free. If not, they will charge your $199 to make the exchange. (note Apple doesn't replace the screen, they will give you a refurbished iPod of the same model, so be sure to back up all your data, before bringing in the iPod)
Your other alternative is to have a third party repair service replace the screen. This will probably be cheaper. Use Google to find a local or mail-in repair facility that you like. Note that using such a service will void your warranty. If you get a replacement from Apple, the balance of your warranty will apple to the replacement.