I agree - it's not an 'Old School' RPG. But Origins did not define what an RPG is. It's just one example. From my experiences at the dawn of the computer game age - Bards Tale, Might and Magic, Ultima, The Lords of Midnight, Wizardry and the various Gold Box games were other examples.
About the only thing linking them is that you have a hero on a quest embodied in a story and varieties of crude and less crude implementation of table top RPG mechanics.
In none of them could you wander off and do or be what you wanted. Neither could you in the later games like Dungeon Master, Daggerfall or Arena. In some, there was barely any depiction of the world at all beyond linked story settings. Or npc's to speak of.
The Quest is the central feature of fantasy and has been the central feature of fantasy rpg's since the beginning. It's simply nonsense to say a 'true' rpg has to allow you to step away from the story. You are always a character on a quest. Most classic crpg's simply do not permit you to step off the story path. The Gold Box D&D ones being a case in point and don't even try to tell me those weren't True Scotsmen, I mean CRPG's. The characters I created in those and played through several huge adventures remain with me to this day.
Does DAI deliver a quest? Yes it does. Does it deliver memorable characters, including your own. Yes it does.
The question of mechanics remains. Is it a necessary definition of an rpg that it has an implementation of old table top mechanics with a vast series of user changeable numbers that shape gameplay outcomes? Furthermore is it necessary that these numbers dynamism and user control does not come wholly from equipment, spells or other external factors?
No - it's about having the options to shape the character mechanics and DAI delivers that through itemisation and skill trees.
Once you look at the crude simplicity of tactics, combat, character and magic systems in classic CRPG's it's very hard to believe that the difference between DAI and DAO stops the former being an RPG.
There's a third essential component of an rpg which is nothing to do with mechanics and that is the player experience, which is a personal thing. Does the setting in specific and the game in general emotionally engage the player? Do they feel they are playing a character?
For me with DAI - I do and no one can tell me otherwise. This is nothing to do with day and night cycles, npc conversations or any technicality. It's about how everything from the visuals, the audio, the companion characterisation, the story, the choices and the details of the background embodied in the codex draw me into the fictive dream.
Just as the crude pixels and crude mechanics of the Pools of Radiance also drew me in.
So yes - DAI is every bit as much a CRPG as DAO (which I also loved). It's just different in some ways that don't impact on what a great RPG experience it is delivering for me.
It's got the questing, it's got the mechanics and it's got the world setting - it's got everything I expect crpg's deliver.
The fact that it doesn't deliver what others were expecting, what others wanted, or what others imagine should have been possible isn't the point.
It means you don't like DAI, not that it's not a True Scotsman.
You might not like the pattern of its kilt or the colour of its sporran but it is.
And for me it's pretty much the best CRPG I've played for a long time.