The way I see it is like this: the word "riddle" right now has been distorted in such a way that it's almost a form of bullying. Puzzles (which used to be riddles) have defined statements at the beginning of the puzzle that eliminate all other possibilities except for the one "correct" one. These days, people make up riddles with only one answer but don't limit it to only one answer. These are bad riddles. Teachers love to use these in classes, making up bad riddles like this in order to convey a certain kind of feeling or, "put yourself in the characters' shoes."

But if it does such a thing uniquely and helps makes the students/whoever understand the point better, then it must be a good riddle, right?

Well, that's where your mistaken. It's still a bad riddle, because when isolated on its own from the 'point' you're trying to make, it doesn't hold up.

Good video games hold up on their own. Fighting games hold up not because of story, but because of their mechanics (I hate the word 'gameplay'). Our problem is that we are so desperate for something to legitimize our hobby we miss the forest for the trees (I think I'm using that expression correctly). We're calling "games," (if such a term can be used) like Dear Esther good, not because they're actually good games, but because they have an amateur story that literally could of have been in a book.

On the subject of if it makes games better: We seem to be so desperate for the feeling of a "good story" that we only focus on that. Games with mediocre systems and mechanics or completely non-innovative ones get lauded for doing something that thousands of games already have, because the "story," is "good" (though it very often pales in comparison to even the most summer blockbuster-y action flick, like Captain America). Many seem to say that the story makes the games more important and more memorable. However, they also seem to say that games such as Bioshock wouldn't have been memorable if it weren't for their "story," (which consisted of listening to an audiobook while shooting things in the face and then essentially being chided for playing the game like a normal human being, a failing of post-modernism and one of the reasons I hate it in video games and hate games like No More Heroes). Well, if Bioshock wasn't memorable but for its story, maybe it's time to study that statement.