Technically, 80mW should be sufficient because the T1s should only require 63.1mW to produce 120dB (which is more than enough to cause hearing loss), however my experience with the T1s has been that while they don't need huge amounts of maximum power, they seem to benefit from a reasonable amount of power and this may be to do with the voltage swing and/or available current required as marshallmole said. Power output can be split between different ratios of voltage and current as I understand it so perhaps the soundcard is producing sufficient voltage, but not current or vice versa - this is getting beyond my technical knowledge, but I know what I've heard and the TH-900s seem to thrive on less powerful amps while the T1s need a bit more juice in my experience.
Technically 80mW is more than enough for T1. The problem is the spec sheet of an amp does not give the clear picture of how it actually performs at a given load.
The important aspect of an amp is how it can sustain delivering the same level of power all the time not just the spike at a given load.
As an example, my Hifi-M8 according to spec sheet is capable of delivering a 1000 mW typical and 1400mW max. But it didn't say at which load. However, they provided the voltage level in each gain settings.
At first glance you will think that it is more powerful than say an O2 (which delivers 83mW @ 600 Ohm load). However, in practice the O2 can drive the T1 louder and has more control over the M8.
At 2.5X gain I seldom need to turn the volume knob past 3 o'clock on O2 (source is DX90 at 1.7Vrms output) or it will be painfully loud. I would get the same level in my M8 only at high gain and also at 3 o'clock position of the volume knob. But it still feels the O2 has better control of the T1's diaphragm than the M8.
O2 didn't even need the full 80mW to drive the T1 with authority in this case (roughly around 30mW with DX90 at 1.7Vrms output and O2 at 2.5X gain)
As for the Hifi-M8, again the voltage spec is useless. As per actual measurements done by innerfidelity.
http://www.innerfidelity.com/content/trusted-traveling-companion-centrance-hifi-m8-portable-headphone-ampdac
At Max gain the M8 is capable of delivering +13.9 dBV. If my math is right, it would translate to 40mW of power @ 600Ohm load.
It only goes to show that we should not take amp spec sheet at face value. One may seem powerful enough than the other but performance can be quite the opposite. But the math is alway right.