No. Games do not "need" stories. Angry Birds is doing just fine without my help. Mario isn't going anywhere. If the argument is about whether or not a game "needs" a story, then the argument is over now. No, it doesn't. However, saying that games "should" or "shouldn't" have stories is like saying that paintings "should" or "shouldn't" use the color red. Sure, not every painting needs red, but just because we don't "need" it doesn't mean that it's smart to dismiss it as superfluous. Whether or not you "should" have a story depends on what you want your audience to feel.
The reality is that a story is just a tool, both in form and function. Just like your aesthetics are a tool, just like your sound is a tool, your story is just another, equally useful tool for ensuring that your game gives players the experience you want them to have. It's nothing more and nothing less, and the sad reality is that, whether or not we like it, thanks to companies like Naughty Dog and Bioware, stories are now a part of the designer's tool kit. Chris Klug and Josiah Lebowitz ran a survey published in 2011 asking gamers, among other things, to name the top three reasons they purchased a game. Story ranked in at #1, with over 52% of respondends claiming that a story was one of the three most important things about a game. Gameplay features was #2 at 42%. Stories may not be important to developers, but stories are important to players, and ultimately they're the ones keeping the lights on in this place.
Not every game will need a story, but not because stories are some strange, mystical beast that is entirely separate from game design. Not every game needs a story because a story is just a tool, and you're not going to use every tool in your toolkit for every single game. Minecraft didn't need advanced graphics. Limbo had no music. I'm not here to tell you that every game will be improved by the presence of a complex narrative. What I am telling you is that stories are here to offer you an advantage, and they're here to stay; whether or not you choose to use one for your current project isn't a simple "right" or "wrong" choice, but simply brushing them aside as superficial is most certainly not in your best interests.