Just to clarify, I used "bad" as an example in my post, but "bad or "average" perspective wouldn't have affected my vote. Probably cuz my brain is still so old school, lol. I sound old every time I say it, but back in the day games didn't have much (if any) story, so what determined if you played a game was based on gameplay, and I guess that just hasn't changed for me.
I also think about replay value. Like, what leads me to playing the game multiple times. With the story I'd play once, maybe twice just to fully understand the story. After that I'd just be skipping through the dialogue/cutscenes anyway. But I think it ultimately comes down to an individual's mentality on video games in general.
I hear a lot of people talk about being "immersed" in the story or game world or whatever which I personally would associate with books or movies. For me it's like if I wanted a movie or book experience I'd watch a movie or read a book instead. Mind you, I'm not a fan of either of those things anyway. Don't get me wrong, I'm always down for good story/characters, but it's never a deciding factor for me.
I'm one of those "mechanical?" type of gamers if that makes any sense. For example, I love the story & characters in FF7 (one of my favs of all time). After escaping Midgar I'm excited to see what happens next in the story, but my mind has even more fun thinking about what setup I'm going to use to be able to obtain the Enemy Skill "Beta" from the Zolom this early in the game.
(Okay, let's give the Elemental Materia to Barrett since he has the highest HP. Put it on his armor linked to fire. Have Aerith's Limit Break on standby,etc.)
tl;dr
Short and sweet version is I enjoy games the most when they put my brain to work. I love to experiment with different ways of playing. Whether it's different setups (like what 4 classes am I going to choose in FF1) or self-imposed challenges (like a low-level run,no item run,etc.) I like thinking about what problems I'll have at certain points in the game and figuring out how I'll get around them.