This is really something that applies more to micro games then larger games. After all, a micro game is not going to be more complicated or deeper than a larger game. Well, at least it really shouldn't be! If that's the case, you're probably picking the wrong larger game to compare it to!
Really, with larger games, the time factor isn't as stringent. I'd go with how many interesting decisions I get to make during a turn. Even that isn't that good a formula. After all, some games, like Macau or Le Havre, are really about building up to making those big decisions.
But it still a decent rule for judging micro games.
There are any number of games that I could use as an example for the rule. Pico 2 or Love Letter are both examples but I'm going to go with Button Men, a quirky little dice game designed by James Ernst.
Button Men is one of those games that is much better in play than it sounds like it has any right to be. Stripping all of the chrome away from the game, which really doesn't serve any purpose other than to give them an excuse to add a picture to the buttons are cards, Button Men is a game about capturing dice.
Short version, each player has a collection of dice that is determined by their button/card/character. You use your dice to capture the other guys dice by either using one die that has a higher number or two or more dice that add up to exactly the number of the die you're capturing. Every die that is used to capture another die is then be rolled, shifting the playing field.
There is always at least one interesting crucial decision to make in a round of Button Men, generally two or three. However, since you can usually knock a three-round game out in five minutes, that's pretty good.
Was I engaged during the game? Do I feel like my decisions were important to whether or not I won or lost? Did I have fun? Did I feel like I played a game? I ask myself those questions for any game but I really feel that if I can say yes to a game that takes five minutes to play, that's a big deal.