There's nothing that ties a blockchain to proof of work. Proof of work just just one consensus protocol. For instance, JP Morgan's Quorum is working on Raft based consensus. https://github.com/jpmorganchase/quorum/blob/master/raft/doc...
The key trait of a blockchain is that each new entry cryptographically verifies all previous entries. At the end of the day, yes, a blockchain is a distributed db. It's a distributed db that never forgets.
I see what you're saying. Basically: distributed database + signatures + merkle tree = blockchain.
I usually use this definition: decentralized and sybil-resistant database + signatures + merkle tree = blockchain.
So I think the key trait that turns a distributed database into a blockchain is not the merkle tree, but is its decentralized nature. Anyone can be a transaction validator and no one can prevent transaction validation.
Consider: a Starcraft 1v1 ladder match is, by this definition, synchronized using a "blockchain", whose participating nodes are the two players' computers and the auditing ladder-server instance. That's not a reductio ad absurdam; that's actually what you should be picturing when you say "blockchain" generally: participant nodes, an event stream chunked into blocks, and a consensus mechanism for validating blocks.
Proof-of-work is just one consensus mechanism for blockchains. Mutually-agreed arbitration oracles (as above) is another. First-claim using a global hierarchy of signed-timestamping servers is a third. Etc.