Quaid: "Well, if the definition that we are gonna use for game is 'you control an avatar in an environment', then yes, I suppose Gone Home fits that criteria.
I still don't believe that is an adequate definition of a 'video game', but I'll agree to disagree."
I agree, that's not an adequate definition of a video game. There are lots of games that don't feature a specified protagonist. But putting you in someone else's shoes with a goal to achieve and the tools you'll need to achieve it is an extremely common game trope. That's why it's easier to identify whether something is a video game or not than it is to come up with an all-encompassing definition of what makes a video game.
Here's what Wikipedia says:
"A video game is an electronic game that involves human interaction with a user interface to generate visual feedback on a video device."
And if you click on "electronic game", you get:
"An electronic game is a game that employs electronics to create an interactive system with which a player can play."
That's actually pretty close to the definition I gave. "An interactive system in which a player can play" is telling because it basically says if you're playing it, it's a video game. There is no implication that elements such as fail states, competition (vs player or the game), or even "being challenged" (whether that's your reflexes, your coordination, your puzzle-solving skills, your lateral thinking, etc) are requirements for a video game.
Now you can argue that these definitions are designed for the layman and do not do an adequate job of explaining what video games actually about, and I might agree with that. But then you're entering the subjective zone where what YOU think makes a video game isn't necessarily what someone else thinks makes a video game. You can say "this is not a game because X", but if you just made up "X" because "feels", then it's obviously going to be debatable. Besides, I repeat that you have yet to give me any practical purpose to making this distinction (at least, any purpose that couldn't just as easily be served WITHOUT making said distinction).