Medium is interesting.
I kind of think of it as the YouTube of writing. Before YouTube, there were a ton of video sites (NewGrounds,eBaums World, etc.) which hosted user-generated and more professional video content, but now YouTube has consolidated almost all of that onto one easy, ad-friendly platform.
Medium seems to want to do that to the blogging/writing world. Before, people had their own websites. Now, it’s a lot easier to just start a Medium, and there’s an ecosystem waiting for you. Plus, they’re using respected publications (The Ringer, The Awl, Pacific Standard) to bring in new readers, add legitimacy, and potentially convince more of the publishing world to move off the web and onto Medium.
So they’re just another platform recreating what was once a feature of the web. In this case, blogging and publishing.