That's a far more complicated question than it sounds - mainly because it requires us to define "traditional marketing". I know that sounds picky, because we all know that "traditional marketing" is everything except digital marketing. But from my perspective, digital marketing is actually a subset of traditional marketing - it's just grown into huge prominence (with good reason). It's never going to 'replace' traditional marketing.
Let me explain - traditional marketing has always been about establishing an optimal marketing mix. It's about reaching your target audience through the most appropriate channels - TV, radio, direct mail, print media, PR, etc... But in the past couple of decades we've added a huge swathe of additional potential channels - web sites, eDM, social media. And not just to push out advertising, but to truly engage with your audience.
So in one sense traditional marketing has just been radically expanded.
However, if I understand your question rightly, I suspect you're really asking if old marketing/advertising channels are becoming less and less relevant.
Again, I would argue that "it depends". Horses for courses. When you take a look at the advertising that's on TV these days, most of the big brands are still there. For those with the budget and the appropriate audience, mass media can still be a valuable part of the marketing mix.
But there's an increasing number of smaller businesses who are now able to compete against bigger players and reach an audience on much smaller budgets than was (is) required for mass media advertising. So we now have a much greater level of marketing activity across the entire spectrum of businesses.
I certainly believe that digital marketing is an imperative for virtually every business these days, whereas older/mass media advertising formats are not as universally applicable. It's also much more accessible no matter how large or small your business is. In sheer numbers, there are a lot more marketing/advertising consultants/agencies/providers competing for your digital marketing business than there is for other forms of marketing/advertising.
But I don't believe that most of the 'traditional' advertising channels are of any less relevance today (with the exception perhaps of advertising in niche market magazines - these are typically struggling to maintain circulation of their print editions and the audiences are largely moving online). Radio, TV, loyalty programs, PR, event marketing, etc... all continue to be an essential part of the marketing mix for numerous businesses IF they are targeting those audiences and have appropriate budgets. We just need to understand how much exposure each of these channels will actually get.