So I tested the headphone EQ profiles more heavily, and did find out that the EQ applies to
all sources, not just surround/spatial audio sources. The goal of the EQs is to provide a neutral sound profile. Depending on your preferences, this can be a good or bad thing. For instance, I
despise the sound of the audio technica m50x (was my first "decent" pair of cans because they came so highly recommended, never much cared for em). The EQ profile in the DTS app made them sound leagues better for everything from music to games. If you have a headphone that's already closer to neutral, you may not notice the EQ without specifically testing for it (this is why this eluded me for so long as I'm almost always using HD 6XXs which are way closer to neutral).
The EQs actually sound remarkably similar to the ones I've played around with
from here, which sound fantastic for the relevant headphones in my testing.
So yeah, if you want your headphones to sound more neutral in
all situations, use the relevant EQ profile in the app. If you want your headphones to sound exactly the way they shipped, use the generic in-ear/over-ear mode.