I'm writing an essay and possibly making a youtube video on the subject of the definition of videogames

In Wario Land II there's no fail state. You just lose money or inconvenience yourself. It's one of the best videogames I've ever played. Your analysis is simplistic and innacurate.

Losing money and inconveniencing yourself is failing. Being helped up with no actual repercussions isn't.

I'd choose a topic that's not the definition of "video game".
"Game" as a category itself is incredibly poorly defined, since playing a pen-and-paper RPG, reading one of the more railroad-y Choose Your Own Adventure books, and throwing a ball at your dad/brother/friend all end up in the same bucket.

A much more fruitful endeavor would be the taxonomy of interactive media, which is also more fun to explore anyway, since you find shit like Tennis for Two, which military scientists played on an oscilloscope when they weren't busy keeping the nuclear defense systems online.

I'd do my own homework instead of coming to Holla Forums and expecting them to help me/do it for me.

Games contain failure states that lead to game-over. There is an aspect of player performance to them.

Is classic "game of life" a game, according to this definition?

It's interactive, but very limited. Besides the college vs career at the start, I don't remember much in terms of decision-making. Whatever career you choose could lead to bonuses, but those are random as well. Moving plastic pieces about with your hands or spinning a wheel are still considered forms of "play" in colloquial terms.

There's competition, in the sense that players see who does better by the end. However, the struggle comes more from the randomness rather than actual competition.

I'd say it is, but it's a poor game. Same as an electronic Rock-Paper-Scissors. At least RPS has an element of psychology to it when done in person, but electronic is pretty much random.