You are absolutely correct. This is about two other things.
1. Forced endorsement of their relationships. They want to legally require that everyone pretend that their domestic partner is their spouse. There is no such thing as same sex marriage. It's like legally mandating Santa Clause.
2. Crush dissent. We're starting to see this already. Bakers who have religious objections to baking cakes with two grooms are being sued for discrimination in public accommodations. That's why they want to co-opt marriage. Disagree with redefined marriage? Tough shit, if you do or say anything against it, they'll sue you into oblivion.