It is a trademark not a copyright, and if they don't defend it they could lose the right to later. Airbnb is a very specific combination and isn't a common english word, therefore yes, those letters in any domain name are protected. If it was a common word, like windows, but the site was about cleaning windows then Microsoft wouldn't be able to come after that person given the common english word.
For Airbnb, if they don't defend their trademark, they can lose the trademark and the right to enforce it, so they must go after everyone who is using it that doesn't have permission. And your usage is a direct reference to their trademark so yea you are in violation here. They obviously don't feel like you are being malicious, hence you got a simple polite form letter and a request to comply not something more aggressive.