Is it permissible to fast three days instead of fulfilling a vow to slaughter an animal for the sake of Allah, a vow that was made upon acquiring a house, knowing that the intention was not vocalized?

If the intention is merely to sacrifice for the sake of Allah without uttering a verbal vow, then a vow is not binding and does not take effect except through an utterance that signifies commitment. As long as your intention was merely an intention that you did not articulate, then nothing is binding upon you.