why is inclusion in an often patriarchal/misogynistic and conservative institution as marriage the end-all-be-all of queer rights?

Legal protections mostly. If you get married, you have a right to see your spouse in the hospital. Otherwise, they're just another person even if you've been living together for 50 years. You also have a right to inheritance, the right to receive pensions and 401k, etc etc. An unmarried partner is essentially left with nothing unless explicitly stated in a will and even then they don't have all the legal protections.

Imagine living with someone for 20 years and they get into a car wreck, you can't see them before they die because you're married. You get kicked out of your home because legally you're just a roommate and have no right to stay in that house. Then, all the money your partner invested goes to their shithead parents who kicked them out as a child. None of that would happen if you were married.

Marriage is an outdated contract but the functions it provides are still important to society.

Edit: Obviously I support China but marriage isn't just a "proof of love" or some other sentimental thing.