The biggest selling games of all time has no story. it has a motivation and solid game play.
I did not count Wii Sports, but it's 85 million
en.wikipedia.org/wiki/Super_Mario_Bros. 40 million
en.wikipedia.org/wiki/Mario_Kart_Wii%C2%A0%C2%A0%C2%A034 million
en.wikipedia.org/wiki/Wii_Sports_Resort 31 million
en.wikipedia.org/wiki/Wii_Play%C2%A0%C2%A0%C2%A028million
en.wikipedia.org/wiki/New_Super_Mario_Bros._Wii 27million
en.wikipedia.org/wiki/Gran_Turismo_5 10 million(PSX)
en.wikipedia.org/wiki/Sonic_the_Hedgehog_(1991_video_game) 15million(Genesis)
In comparison one of the best story games sold
en.wikipedia.org/wiki/Final_Fantasy_VII%C2%A0%C2%A0%C2%A010million
are stories awesome yes. Do stories sell games. yes, do stories define games. no. do games need to tell a story, no. do adventure themes games need a motivation yes. (mario bros has no story, but it does have a motivation)
Now of course your stuck with the debatable question. Does financial success make a great game? Indeed that is one measure to use. A financial success of 40million games sold must have something going for it to have sold soo much. People, gamers play and play the game with some games becoming classic.
On the other hand even games that don't sell well can still be awesome games. However there is usually somekind of reason why it doesn't do as well. Marketing, distriution, theme, genre.... however it all comes down to being a whole package and no one factor determines massic success.