We'll need to clarify what you mean by "attracting" women. For initial attraction, game doesn't matter very much assuming you have decent looks/energy/etc.
For keeping women interested, game is paramount. No amount of looks, money, status, etc will make a women sexually attracted to you if your game is ****. They will lose respect (and thus attraction) rapidly if you display low status behavior.
The advice men give to "work on yourself and women will come" is flawed, self development won't make much of a difference with initial attraction except for improving appearance. You need to improve your wealth/looks/status/charisma/etc AND develop game; game is always completely independant.
I will grant that the more attractive you are, the more get away with sloppier game, there is definitely a scale to this. I would also say that women expect attractive men to not use as much game because using game shouldn't be as necessary when you're already attractive. On the other hand, a guy who's more average looking will become much more attractive to them with good game because it basically implies they're experienced and confident with women (also, because they HAVE to use game so women expect it).