إِيمَانًا بِاللَّهِ and تَصْدِيقًا بِوَعْدِهِ show that intention matters alongside the outward form of an act. Where an animal or other resource is dedicated for ongoing service, an initial declaration cannot replace sustained care and fulfillment of its needs.
فِي سَبِيلِ اللَّهِ qualifies the specific religious purpose described in this narration. It gives no permission for harm to others or irresponsible use of an animal under a self-declared cause.
The key lesson is to connect sincere intention with tangible responsibility for living beings under one’s care.