I guess I am not understanding the question.
No, sorry, it is I who have misunderstood. I didn't realize you had the dual-link Apple adapter. I somehow had assumed you were using the cheaper, single-link Apple Mini DisplayPort to DVI Adapter.
So in that case you have shown that Mac OS is possibly not savvy about 120Hz. I suppose the final step to take, assuming you want to try and take this further, would be to download SwitchResX and see if you can put it's features to use. One thing it can do is read a display's EDID. That would tell you if the Asus has a well formed EDID or not, meaning in this case that it is informing the Mac through EDID that it supports 120 Hz. It could be that is missing from the driver (EDID).
The other thing SRX can do is allow for the building of custom timings. You could try manually building a 120 Hz timing and see if it is accepted as valid by the Mac hardware and software and hopefully then the timing will become active and selectable within Displays Preferences.