It isn't clear to me what the purpose of such a legally recognized partnership would be. All the functions of legal inter-human marriage that I can think of are inapplicable. Humans already have the rights to do anything they want to their pets. Giving rights to pets is pointless if they can't effectively claim them (deciding on partner's treatment in a medical emergency, custody of partner's body after death). Tax and property rights - non-humans can't own property or money. Custody of children is irrelevant. Etc.