If women massively died off in the world, there would be instant nuclear war. Society would not continue to exist and just "accept" the small amount of women left. They would be considered a strategic resource and fought over. A healthy woman can, generally, give birth to one baby a year (yes, exceptions exist, stay focused here). Assuming that, for the good of humanity and rebuilding the population, they are forced to give birth from mensus (lets say age 12 as average. Some younger, some older.) till menopause at 45, one woman can give birth to up to 33 children, assuming no multiplies.
That is a slow rebuilding of the population, and thus woman would be fought over, with only the most "worthy" (connected, wealthy, etc) men getting a chance to have a child with a woman. And each new child would probably be with a new father to increase the genetic diversity of the next generation.
Women would be considered property (more so than they are now). They would be secured in facilities under lock and key and guarded against random violence and random dicks.
All the above to say, I have a hard time accepting t he premise of this game as is.