Really all this article suggests is a p2p network where you are paid small amounts of BTC to be a peer (and pay to access other peers) and upvotes send BTC to the poster. It's a ludicrous idea that would never work. Reddit works because, among other things, votes/karma is worthless. Everyone's vote counts equally and everyone can vote on everything once. To tie voting to BTC or incentivize people to scam/cheat/lie for real money is just idiotc.
Also the blockchain will not be used to "host" the new reddit and other people (wrong people) have suggested.
Now an identity linked to the blockchain, used to access a decentralized reddit of nodes that contained subreddits which could be synced to other nodes (think newsgroups/usenet) but with anyone being able to run a node and set retention rates on posts/comments might work. Anyone could archive off bits and pieces of it (a la google groups) but some might only be hosted on 1 node or require some kind of key or password to access the content so "dark" sub reddits. The big problem is voting, and I'm not sure if a system like this could support anonymous voting. I'm guessing not but I'm no expert.