A good game is one that is enjoyable to play. IT doesn't have to be fun just enjoyable. Usually fun is used to be enjoyable but there are cases of games like journey, or so I have heard. Extra points if you get that feeling at the end of a game. I am not sure how to explain it. Maybe accomplishment. Also the game should make up for it's short comings in other areas. Like Mass Effect 1. The combat was meh, but it really made it up in the story and characters.
I disagree with your last point. There are games that got famous off of single player(mass effect(until 3), Elder Scrolls, and plenty others)and there are good games that multiplayer has made them famous(mmo's,rts's, and plenty more). It really depends on the game if we are talking single vs. multiplayer.jbm1986 said:A good game:
-is unique and fun
-is immerse and entertaining
-has fluid gameplay
-is easy to pick up, hard to put down
-has good graphics(not really required but it helps)
-good story
-good music
-interesting characters
-balanced (difficulty)
-equal single/multiplayer (does not favor one over the other as a selling point)