Firstly Ethan split it off. He does do Mod things now and then, and well this all blew up while I was at work.
Video Games are quite easy to define what is an what isn't purely down to the fact it's a video game. It comes from adding the word "video", as in "visual-audio" to the word "game", as in board game, table top game, outdoor games, etc. Not the other way around. A large part of the issue comes down the fact people forget that at the end of the day it's all software, video games have more in common with Excel than they do with other "artforms". Which at the end of the day leads to big huge muddy waters as people try and bridge the gap between pong and Mona Lisa. It's a bit like whales, tuna and llamas. Whales have more in relation to llamas than they do with Tuna, but whales hang out with tuna more often than llamas so people tend to forget of that underlying link.
In general definitions games have rules and objectives, usually with some form of competitive element. Be it video games or board games. It's not necessarily about the interaction. Many things are interactive. It's about the goals and rules. I think everyone can agree Pong is a video game. As is Tetris. Generally if it shares many elements with those two you're golden for the "is it a video game". The more you're lacking in common with these then the shakier ground you're on. I think folks just call stuff like Dear Esther and Proteus "video games" out of laziness to create a new taxonomy. When they reach a certain volume you'll see a new definition crop up for them. Kinda like MOBAs/Dota-likes.
Linger in the Shadows is demoscene. It's about as much a video game as everything on Nvidias page, or the PSX T-Rex demo and such. It's related to video games, but generally it isn't built as a game.
There's also simulations, which are generally also related to, but not actually video games. Kinda sometimes spills into "toys", which (well because it's what he likes to call them) includes stuff like Sims. Not quite a simulation, but overly lacking in clear direction yet still playful, much like a dollhouse in real life. (As opposed to say..a weather simulator).
End of the day it's a bit like defining life. There's always going to be outliers like viruses.