It's an interesting debate to be had, but I think the question in the OP misses the point slightly. You ask why should anyone care about a story if the story is underdeveloped or absent altogether. People probably care because they don't WANT it to be underdeveloped or absent altogether. They want a deep, engaging story with their video games.
I'm of the opinion that storytelling is inessential in video games, although there have been some pretty great games with terrific storytelling: Final Fantasy VI, Metal Gear Solid 3, BioShock, etc. But there are also all-time great games with little or no story: Tetris, Super Mario Bros., Street Fighter II, Mario Kart: Double Dash!! Let's remember that these are meant to be games after all, not interactive movies or storybooks.
I'm reminded of this article from VGChartz: http://www.vgchartz.com/article/250250/dylan-cuthbert-miyamoto-focuses-on-gameplay-first-story-second/
I think it's a good philosophy to have, although I appreciate those who disagree with me.










