@Mark3056 I can't imagine why you'd have to get the entire floor replaced- I've done a lot of tiling myself, and a good tiler should be able to chisel out the broken tile and replace it, assuming that you have a spare or two ( you should always make sure you have a spare). But even if you don't have a spare, you say the floor is only a year old, so hopefully you could buy a replacement.
I can't imagine why they are saying you need to replace the entire floor- that's absurd.
And unless you have some way of proving the guest did the damage, I think you're going to have to chalk it up to wear and tear- you are probably quite correct that they did the damage, but they are denying it, so they aren't going to agree to pay, Airbnb won't pay for a whole new floor, and you'll probably end up with a bad review from them if you try to charge them, so you just have to weigh the situation.