So from the miner's perspective the incentive is there. There's the "wasted bandwidth" angle there as well but that's a different story...
I was asking what the incentive would be to go through the computational effort of creating a block in a system that doesn't involve money. The author gave the example of using blockchain to maintain a shared calendar. What incentive would I have to go through all the computational effort to create a block of calendar entries?
Or let me know if I misunderstood your reply.
There's nothing preventing the same tx fee system bitcoin is using from being implemented even if the blockchain itself is not used to transfer value. So now it is a can of worms, no doubt, as the system would have to have a way of attaching the fee to a "real world" value - along the lines of how Ether/Gas relationship works in Ethereum, but it can be done.
Another thing to keep in mind is blockchains the author is talking about in the article aren't necessarily public - with a private blockchain the nodes are paid for by the organization using it in some way shape or form.