People swear by say a Fiio E11 for 250ohm headphones. The E11's max output is for 300ohm headphones. There are certain headphones like the HD650 which is 300ohms rated, however, with certain ranges of sound, where it suddenly spikes up to over 500ohm, making the E11 'choke' at the sudden jump in power demand. You may not hear it, but the bottleneck is there, in that the impact is significantly lessened to what it should be.
In the case of planar magnetics and rare dynamics like the K702, the impedance curve is VERY linear, meaning there won't be a sudden spike in required voltage, though they do need lots of steady current.
You can always settle for less, but you're doing you and your equipment a disservice by doing so. For gaming overall, using say a K702 with the Mixamp alone is doable, because the virtual surround processing masks imperfections. That and games don't tend to have the best sound quality to begin with. Still, you won't be tapping their potential whatsoever.
Edited by Mad Lust Envy - 1/29/13 at 3:10pm