Think about it: if you have a website and are putting out content on it, like I always talk about, you are blogging. Twitter was flat-out known as a micro-blogging platform and now we have new platforms like Medium that point very strongly to being a blogging platform.
I would even argue that Instagram is a form of blogging in itself; A visual diary for your life. Or, Snapchat serving as a blogging platform built around the promise of content taking 10 seconds or less to consume.
So no, blogging is not dead. It's as alive as ever. Blogging has simply morphed and changed into a much broader category where blog creation, and the question to where you should be starting a blog, is very different. A stand alone independent website run on a wordpress blog or something similar isn't required anymore. My advice would be to just start putting out native content on the platforms that make most sense for you and start engaging with those who you think should see it.
But here is the problem and reason some internet marketers might say that blogging is dead: people who are still blogging in the traditional way, by posting to their personal website, don't know how to get people to come see what they are writing. Nobody is working hard enough to master the art of SEO, or Facebook dark posts, or Pinterest, or storytelling on snapchat or anything else that can drive to your page.
Starting a blog has never been easier and here is where to start a blog: Snapchat, Twitter, Facebook, Medium. Now, I know what you're saying — “Those aren't blogs”. Actually, they are. Any social media platform can be treated like a blog because that is where people are listening.