Personally I would probably care less about the appraisal. As others said, there is a hassle factor of starting the home search over again.. & clearly you were willing to pay the agreed price. (& on the flip side, there were so many appraisals that were wrong and fraudulent when times were good - it never meant much to me).
So how does the lender feel about this? OR are you paying cash? I mean it doesn't really matter what you think - it could jeopardize any potential mortgage loan?
All of the above said, from a negotiating standpoint, I would consider walking away. Personally, I think the sellers are dumb not to budge. Selling a house that has appraised for $10k less is a tough sell, and most lenders will take issue with that. I'd be tempted to walk away and call their bluff. But I am not in the situation so is harder to read from afar. I could also see the flip side that it doesn't really matter, *I LOVE the house, it's perfect for our needs, and why risk losing it?* In this type situation I have walked away many times and WON! When it was clear the seller was just way unrealistic. BUT, not when it comes to a house. Both sellers and buyers get very emotional when it comes to a house - so I'd be less optimistic that would really work. I know too many sellers who rather their house sit empty for years and go broke than sell at the true market value.
So the thought crosses my mind to call their bluff, but maybe they aren't bluffing.