In general I agree with what you're saying and I think that your second definition of sexism is very insightful and something everybody should consider and think about (even if they ultimately find they cannot support this definition).
However, I would like to point out that whether being "male" makes you play life on easier difficulty than "female" depends to a large extent to how you weight different outcomes of the game. While it's probably still true that being male makes it easier to earn more money (especially now, when all the geeky, previously unpopular, mostly male programmers cashed in), but it also makes it easier to be homeless and to die sooner (homicide/suicide).
However, I would like to point out that whether being "male" makes you play life on easier difficulty than "female" depends to a large extent to how you weight different outcomes of the game. While it's probably still true that being male makes it easier to earn more money (especially now, when all the geeky, previously unpopular, mostly male programmers cashed in), but it also makes it easier to be homeless and to die sooner (homicide/suicide).