I'm afraid your question should make any self-respecting English teacher exclaim a loud "harumph"! LOL! Regardless of the advancement in technology of our age, one is not considered "learned" unless they have a basic knowledge of literature. Yes, we use technology, but without the fantastic basis of literature, what on earth would we use technology to talk ABOUT.
Even before literature was written down, humans spouted literature orally, often telling stories to teach a particular moral or value. Just off the cuff, ... I'm remembering the ancient story of Midas, the man who could turn all he touched to gold only to die of starvation and thirst. The first warning against materialism? Perhaps. Fast forward to the 1920s and you have The Great Gatsby suggesting the same thing.
If you'd like to switch over to pure entertainment value, look at the Harry Potter series that taught SO many youngsters to love reading. And then there was the Twilight series that taught SO many teens to love reading. (Ha!)
Literature remains one of the few ways I know of that we, as humans, can truly lose ourselves in another world. In literature circles, we call this "suspension of disbelief." We put our disbelief on hold for a while in regards to a story so that we can immerse ourselves in another life. All good literature should allow us to do this.
So, ... let's compromise: grab a Kindle and READ. : )
Just because we have access to more and more technology doesn't mean that our desire for literature is fading. I would just look at the proliferation of e-readers on the market to suggest that two things compliment one another greatly. We may be reading about different things and in new ways, it ultimately words on a page to communicate an idea, and that doesn't seem to be ending any time soon.
I think there are all kinds of things in literature that are still relevant, and if you consider a rather wide range of books to be literature, even more are relevant.
If you read any science fiction, it is still a wonderful place where the moral and ethical questions raised by powerful new technologies are raised and dealt with. These can be particularly helpful to those willing to pay attention to them as our society generally fails to raise these questions and rushes headlong into any new technology without pausing for breath.
I would argue that literature is relevant to today's generation in the same way it was relevant to my own (born in 1970) generation.
Literature has always been relevant only to those who care. Literature has been (at least since my youth) an optional thing. You could easily go through life without truly encountering "good" literature. I think it is the same now.
For those who care about it, literature continues to be relevant. It continues to allow people to explore and contemplate the human condition. That, too, has not changed.
So I guess I don't see a real difference between literature's relevance today and its relevance to my generation.
Literature and technology are not mutually exclusive. In fact, with the use of technology, literature can reach a far wider audience than ever. Technology is merely a vehicle - literature is the passenger. Literature remains a great unifying and illuminating force - one of the ways in which we learn and celebrate ideas, share experiences, connect to our pasts, gain insights into other cultures and share in hope for the future.