first, he has alc892 onboard not 1150. while true that high end boards with good onboard audio should handle his headphones fine it seems like he has rather cheap onboard sound which may not have a very good amplifier.
second, an amplifier is not for improving the sound but increasing it in power so that it may move harder to power drivers. while a good quality amplifier can certainly sound better than a lower quality one thats a different thing entirely.
the zero is rated at 150ohm impedence yet has fairly high sensitivity. if they were low sensitivity then i'd say an amp would be required although since they are high sensitivity its a harder call. given the low quality soundcard onboard and the fact that the zeros are fairly decent i'd say its quite worth getting a soundcard.
vx, i'd say it would be worth testing them on the onboard on your pc before making any decisions however i think you could certainly benefit from a soundcard.
the xonar dg would be a cheap option and has a strong amplifier. or, you could run the xonar dx which gives you a better dac and just run an external amp if you need one (though i think the dx should be capable of powering them even though it has a weak amp). the creative z is also a good choice and has a strong amplifier (although perhaps a bit too strong, expect to run volume settings at very low with it). as for externals there are things like the u7, omni, etc which work.
if all you wanted to do is boost volume levels (and didnt care about increasing quality with a better digital analog converter (dac)) then they do make external amplifiers only (such as ones by fiio) which work. even one of their cheaper products would work.