In the end, you would marry her because you want to have sex, and that's pretty much it, no other incentives right or in the long run. Also, from what I understand, you are ok with having an informal relationship with her.
So what's the point of a marriage in your case? If she's dead serious, it's time for a talk, which I personally doubt. Someone else here said that you should wait 3 weeks and after that she will have forgotten about her supposed ultimatum. I'd do this.
My bet with The_Liquid_Laser: I think the Switch won't surpass the PS2 as the best selling system of all time. If it does, I'll play a game of a list that The_Liquid_Laser will provide, I will have to play it for 50 hours or complete it, whatever comes first.