But the specific point is that it has both you interacting with the game, and the game interacting with you, and having those interactions feed off each other.

It's a binary choice that leads to an audio blurb with a couple "hidden secrets".

I don't see how that can be considered "more interactive" than a game where you can pick up just about anything, where you can go pretty much anywhere in the game's world, and where you are basically free to engage however much you want into given story threads.

Gone Home doesn't chime in to say "Congratulations! You did option 1, 2, or SECRET. I will now be happy and continue my story, upset and passive aggressive and try to continue my story, or tell a joke about glitching outside of level boundaries." But to pretend that what you do get for exploring and interacting isn't the game "interacting back" as much as getting static linear audio content as a reward for your path seems ridiculous.

Stanley Parable's means of interacting with the player is cheap and obvious. That's the point, its existence is a joke and that joke is that the game lacks meaningful interaction. Stanley Parable's core thesis is that you can't meaningfully interact with it, and what does that say about choices in other games?

Calling it a hidden third path isn't even accurate considering that's part of a linear room.

That "linear room" is, mechanically speaking, just part of the "hallway" leading up to the first choice. In game design terms, I'm using "hallway" to refer to linear game content leading up to a choice point. Hiding that "third option" anywhere in the hallway leading up to Left or Right counts as a third path.

Otherwise: Cool, that brings that room up to the same number of choices as a normal room.