Read my post please. I did the 250w calculation, but the mistake you are making is that you don't have control of the load impedance. You have a fixed load (your headphones) that you are trying to drive, and it is the same no matter your source. To deliver maximum per to a fixed load, you want as near a zero ohm source as you can get.
Or, to put it more simply, with a given load and power supply, one will not be able to output more power to the load by adding serial resistance*. That should be easy enough to see.
With an amplifier that has very low measured output impedance, matching it with the load does not necessarily give the maximum power output, even if overheating issues are ignored. In fact, it is rather unlikely with typical amplifiers because of current limiting and much higher open loop (without negative feedback) output impedance. Strong negative feedback reduces the output impedance (and power supply impedance, etc.) as it appears to the load by orders of magnitude, but those "hidden" impedances still count towards determining the maximum power output.
The theory of matching the load impedance with the source can "work" for maximizing the power transfer when there is a high output impedance (e.g. 100 ohms in the case of
this sound card, or hundreds of ohms on the headphone output of many receivers) from an external resistor that is outside any feedback loop. However, that is not something one would normally consider a good amplifier design.
* In some uncommon cases, this can actually be useful by reducing the power dissipation on the amplifier (as some of the power at the same current output will now be dissipated by the resistor instead). However, it is a better solution to avoid the resistor, and increase the power dissipation the amplifier can handle without overheating instead, for example by improved cooling.
