These remind me so much of Creative's Marketing for it's EAX Soundcards over the years, it's uncanny. Ultimately alot of the effects they boasted were EQ manipulation, but eventually as the hardware improved in the soundcards, they sounded better leaving it all turned off.
If it simply is an EQ, then the best one i've used is free: Equalizer APO. People have uploaded profiles onto Github for the majority of headphones on the market. However that's not perfect. I have a 72 point Parametric profile for the Amiron Homes, and that's still less effective than swapping pads on Beyer Headphones.
The makers of Iris stress though that it isn't an EQ, but mathematical fomula/equation, in which case it sounds similar to the optional resampling in JRiver Media Center that they have been doing for years.
In terms of applying the software, I can see this only working if you are using USB/Bluetooth to make use of the onboard hardware. When using the 3.5mm jack, it will be an analogue signal by that point in which case the headphones would work like any other by that point like Bose Quietcomfort and the Sony WH-1000X series.