Hello!
I think the question of what makes a good game is extremely important. I know many people REALLY need exciting gameplay, or gameplay which is at least involving.
For me, the story is probably one of the most important factors. Of course, in a game like League of Legends you cannot expect much of a story, apart from the nuggets of lore which the developers create, and I do not expect there to be much. However, even then, the pieces of storytelling that ARE there win over my soul.
It's part of the reason why I love Dragon Age, from Bio Ware, since the game is SO rich in lore, culture, religion, spirituality, politics, war, conflict, personal growth... it involves not just my brain and reaction time, but my mind and heart.
I'm doing a play-through of Dragon Age 2 now, which I've begun to upload on here. Everyone is welcome to come and join me.
But yes... the Story and the Plot are really important for me. As well as how much impact I have on the game world as well. That's a winning factor for me. (Skyrim falls into that, since all the decisions you take in game barely have any visible impact on your surroundings)