You have already posted that 22.5 kHz is technically ultrasonic, using the link in your post even Wikipedia says it is.
First, the upper limit for your Tinnitus Mix file is 22.05 kHz, not 22.5. Second I have not stated that 22.05 kHz was ultrasonic, and Wikipedia doesn't say it is either.
What 22.05 kHz is is the lower bound of the ultrasonic range. That means any frequency above that is considered ultrasonic. The Tinnitus Mix doesn't contain any frequency above that, due to the 44.1 kHz sampling rate (by Nyquist-Shannon theorem).
They do when your signal contains energy at those higher frequencies, which is not the case for the Tinnitus Mix.As for the frequency output graph shows it just doesn't stop at 22.05 kHz, yes it is much lower but some higher frequencies get through to Koss headphones.
48 kHz is a common sampling frequencies too (for example, for DVD sound), and had that been the sampling rate you had used, you'd have been able to encode frequencies up to 24 kHz, which would - according to the frequency response graph you quoted - be able to be reproduced (albeit with significant attenuation) by the headphones. That would have allowed a tiny bit of ultrasonic range to go through, if the playback equipment (computer, mobile, etc) had all the necessary hardware to reproduce it (the DACs, in particular).
There is some sound equipment that samples even higher (96 kHz or 192 kHz).
There is no magic with very short pulses. The Tinnitus Mix doesn't magically transcend the laws of physics or math.You also must consider the very short pulses on Tinnitus Mix that act differently than audio waves.