Parcheesi first entered the slang as a reference to sex as a result of a scene in the 1964 Aubrey Hepburn film, Paris When It Sizzles.
The two main characters (Rick and Gaby) are discussing a scene when two people start kissing and "...". Gaby mentions that she doesn't know why writers do that, because everyone knows what the couple is actually doing, but Rick the writer replies that she has a dirty mind, and in all reality, the couple in question was just playing a game of Parcheesi.
Since that point, Parcheesi has been a widely used, if not somewhat subversive reference to sex. Many refute that the film started the reference at all, instead pointing to the sexual undertones of the game itself, but this is unlikely.
Why don't you come over for a nice long game of Parcheesi? -- bow chicka wow wow!