Looking at the specs I'm a little baffled. Even on the balanced output the power seems low. I'm assuming it does more than the single ended... but only one 6922 on a balanced amp? Strange. I'm also seeing a x8 (18dB) gain listed here but a maximum of 1Wrms at 50 ohms? This should be getting it near 5 watts at 50 ohms (if not a little more) per channel. All of this is just strange. Is the voltage reaching its potential at higher impedance? I can't tell from the specs because its not listed.
If someone can tell me what's actually going on with this amp I'd be happy to know.

I am pretty sure the balanced out is just a connector, not an actual balanced out. I don't understand the rest of your post. Gain has nothing to do with max power output. Where does your figure of >5W into 50Ohms come from?

For power the answer goes to into input voltage x gain = output power. In a perfect class A scenario this would mean 2v input x8 would equate to 16v output. If you divide that by 50 (where this amp is listing its 1 watt rating) you get 320mA of current at that impedance. 16v x 0.32A = 5.12W. This amp is very current limited accounting for this math.
For 1 watt to be the limit at 50 ohms the current limit would be about 150mA. I'm assuming the power available at higher impedance is much better since you don't need 150mA to output 16V at 600ohms.

For loads >50Ohms most SS headphone amps are going to be limited mainly by output voltage (not current). Using gain to extrapolate power output makes no sense because, as you've noted, it will hit the rails first. It gets 28V DC from the power brick. While it's possible they step it up for the current gain stage, I doubt they do, in which case max output voltage is going to be less than 10Vrms.

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If someone can tell me what's actually going on with this amp I'd be happy to know.

For 1 watt to be the limit at 50 ohms the current limit would be about 150mA. I'm assuming the power available at higher impedance is much better since you don't need 150mA to output 16V at 600ohms.