Well, it's more of a thought exercise than a game, but nonetheless, very interesting and you should give it a whirl! "It" being a web version of an exercise we did at the annual MIT LGBTQ student leadership retreat in Provincetown. Thank you to the MIT student who put it online!
Before you try it for yourself, keep these things in mind for the different scales:
Sex: Contrary to popular belief, sex is not just your genitals. Your secondary sex characteristics and other parts of your body can also be count as parts of your sex. For example, some people with vaginas have very small breasts and some people with penises have very large breasts. Some people have vaginas but no ovaries...and so on. While "M" and "F" are usually presented as "opposites," it's not that simple, even for those who don't identify as trans or intersex.
Gender role: Where do you see yourself on the scale of masculinity and femininity? To you, what do those "M" and "F" poles represent? Who is the most masculine or feminine person you know? How do you compare to those people?
Perceived gender role: How does the world at large perceive your gender role? It's interesting to see how much this does or does not match up with what you assigned for your personal gender role.
Sexual attraction: This is vague terminology on purpose...sure, who you sleep with is a big part of determining where your dot goes on the scale, but think about your past crushes, the range of people you gaze at on the street or in magazines. And don't forget your repressed fantasies!
Perceived sexual attraction: What do people generally presume about what types of people you are attracted to?
Once you finish, you can see your line and that of all the others who have participated. If you have the time, trace a couple of the other lines and see where they lead! Happy gender/sex/attraction-ing!