Earlier quoted context omitted.
having proof of work or not is orthogonal to whether it's a blockchain or not. see: blockchains for proof of stake cryptocurrencies.
I think a lot of non-technical business people and journos didn't fully understand that the Bitcoin blockchain is more than just a Merkel tree, and so have started using "blockchain" to mean a bare MT, despite the fact that the blockchain in Bitcoin is only meaningful because of how it's computed. So maybe proof of work can be replaced, but without some consensus protocol it's not a blockchain in any meaningful sense…
I pretty much agree that "some consensus protocol" is probably the right place to draw the line. I'd add "decentralized", in the sense that no single entity can control the "consensus", which I think may be what you mean: "some decentralized consensus protocol".