I did enjoy that video he made, but I don't think a lose state is the be-all-and-end-all.
What it needs, based on my list of objective and subjective qualities of a video game, is challenge. A fail state is a type of challenge, but there are many others. That's why LucasArts'/Telltale Games' point-and-clicks (with exception to a couple titles) can be classified as games, even though you can't technically die.
tl;dr Game needs to have challenge to be called a game, failure state (death) is just one type of challenge, but not the main or only one