1.
Super Mario Kart (1992) is very very influential. Not only did it inspire all kart racers, but it was the most successful spinoff game of all time. Sure Mario had appeared in a few non-platformers before this, but they were always kinda random cameos (Pinball, Punch-Out!!, NES Open Tournament Golf, and kinda even Dr. Mario). Super Mario Kart was the first spinoff game to feature an all-star cast, and use power-ups from the Mario universe like stars and whatnot, like the game was a damn variety show. If you look at it that way, it inspired every spinoff game ever. It may not have been inspiring great games, but it inspired TONS OF THEM.
Here's a list at Wikipedia:
http://en.wikipedia.org/wiki/Racing_game#Kart_racing_games
It includes all-star cast styled kart racing games from franchises like Sonic, Diddy Kong/Banjo, Mega Man, Looney Tunes, Star Wars, Mega Man, Crash Bandicoot, Bomberman, and everything else ever. And yeah they almost all suck, but that's because we can't help but compare them to Super Mario Kart, which is the whole point. It's the most influential and still the best.
2.
But after reading the article... this entire list is bullshit. They actually mention SEPARATE CRITERIA for each game. They list Super Mario Kart not for the actual influence I mentioned above, but because "it was the best selling racing game on the SNES, GameCube, and DS." That same logic could put Gran Turismo at the top for being the best selling racer on every PlayStation platform. Tetris is #2 because "it's available on at least 50 platforms." GTA3 is somehow more influential than Super Mario Bros. or Donkey Kong because "it's the most controversial series of games."
They're picking "best selling racer," "most available puzzle game," and "most controversial series," and yet calling the whole list the "most influential games." That's uh, DUMBWRONGBAD.