On the level of 'this annoys me but it's not that big a deal': Triple-I as an industry term has been around for a while and historically would not include most games in the 'III showcase', IMO. To my mind, 'III' implies:
- Either an independent studio or one that has creative autonomy and identity even if it's not independent
- A pretty significant budget and team, but still not at 'AA' level
- High level of polish in a limited scope. I joked that 'III means there's exactly one high graphical fidelity character model' but honestly that's not a bad rule of thumb
- More visually or mechanically experimental than a bigger production can typically afford to be; strong authorial vision; identified with indie trends, aesthetics, or process
This is all very vague, but it definitely doesn't include something like My Time at Sandrock or whatever. It overlaps more closely with 'AA' than with proper indies.
An example might be something like Stray... big publisher, pretty big budget. High graphical fidelity but with clear limitations on scope (eg, no human characters). Experimental, high-concept premise.
Basically: Indie aesthetics or process but at 'A' scale. A category that might encompass some of the bigger Annapurna or Devolver projects.
If you said 'III' to me, I'd think of a category that's closer to including Echo or Returnal than Shadows of Doubt.