You are correct in that a 2nd home is a capital gain to be reported. Due to being held more than one year, it is a long term capital gain, which gets more favorable tax treatment.
As far as the state, goes, I am not sure where you read it does not get reported. Your resident state will tax you on it, and if you paid taxes on the gain in another state you would get credit for it.
Resident states tax your income regardless of where earned, but in some cases a credit can be taken if taxes paid elsewhere. In your case it does not appear that taxes were paid elsewhere.
