For headphones systems, as opposed to speakers systems, there's generally less emphasis on how much power is being output, maximizing power delivery, and so on, because you're not scrapping to get something powerful enough and you're much less likely to fry your system by just plugging different things in randomly. With headphones, we're dealing with power levels in milliwatts rather than watts, for a crude comparison. The above link is thus not very relevant to the discussion.
For the Asus sound cards, the < 32 ohms, 32-64 ohms, and > 64 ohms settings just correspond to differences in volume. For the lower settings, they just limit the volume (digitally). Despite the misleading labels, there's nothing actually going on in terms of the circuit changing, matching impedances, or anything like that. Use whichever.
In general, the higher the impedance of the headphones and the lower the sensitivity, the quieter they will be at a given output volume setting. Thus the three settings are there as some kind of half-baked guideline. Higher-impedance headphones do require more voltage (output volume setting) to be delivered the same amount of power, as you can easily see by P = V^2 / Z: power equals voltage squared divided by impedance. For more or less fixed V^2, if Z increases, P decreases and thus you get a lower volume sound.