The only time his rights can be terminated is if he willingly consents to it or the state terminates them due to him being unfit or if it falls under abandonment.
As you've already discovered the state doesn't allow a parent to just walk away from their legal & financial obligations to their children unless it is so another person can adopt the child and that person is already approved by the court to do so.
Abandonment is X amount of years of no contact, no child support and each state has it's own guidelines on time but it's generally 2-3 years. He is seemingly paying child support and seeing the child so abandonment does not apply here.
Your fiance cannot adopt her because you are not married. For a step parent adoption, you must be married to one of the child's biological/legal parents and have been married 1-2 years in most states. The PAP (prospective adoptive parent) also needs to have a home study done. All adoption types, even a step parent adoption require a home study.
As it stands unless her father agrees to willingly terminate his rights, your fiance cannot adopt her even if you were married. Adoption would need to wait until she is of legal age and able to make the decision for herself (yes, you can be adopted as an adult). 12 is pretty young for her to be able to know what that means and for her to be mature enough to make that decision now.
Her dad seems to be trying here and you need to meet him half way because that helps her. You should be encouraging her to develop a good relationship with him because she needs that. If your fiance loves her as much as you and he think he does, he would also help them with that relationship.
If he's seeking full custody, given his track record he's unlikely to be successful but he may be able to achieve more parenting time with her.