Unfortunately, the quoted article has serious shortcomings and would be unworkable in practice. In the first place it isn't just about blockchain, but also mixes in quite a lot of other things, such as the bitcoin that is usually associated with it.
The article also misrepresents in some ways the reasons why you would want to do this. The financial crash wasn't, in fact, caused because financial institutions had centralized record keeping but, rather, because they had been given unlimited power to manipulate markets by a feckless congress. The medical record example is a bit stronger, however.
But the article also has the following technical flaws.
The school principle can create grading value (points toward grade = bitcoin) pretty much arbitrarily.
The transaction fees would have to be much (much) lower as they overwhelm the possible gain by participating.
Unless the student grader is also a miner, they have no incentive to participate as they can only give up points via transaction fees.
The reward (potential) is not in any way related to the educational objectives, made worse by:
In the real (bitcoin) world, the miners are so busy mining that they have no time to do anything else (e.g. study). The system actually enforces this, by making the reward harder to get over time.
At the scale of a school, miner pools could easily reach 50%, destroying the whole thing. Some students would much rather do search for treasure than do actual academic work. Why reward it?
You replace expertise in the subject (teacher grading) with amateur action, which is subject to error. If it just matching answers to keys with no interpretation, a machine can do it.
The overall work entailed increases as each exam is "graded" multiple times, plus the treasure hunt.
I envision that it would be more difficult for a student to contest a marking error in this scheme, though it might result if fewer of them being made.
Even in this scheme, exam papers can be lost. Distributing them probably increases the risk.
If teacher vindictiveness is an issue, blind grading can be done without the other complications of the scheme. It isn't actually essential that the teacher knows who she/he is grading.
As to the cost, I'm sorry, but if we paid teachers an actual living wage I'd be more willing to accept the argument. But in the real world, teachers don't really work for money. Lawyers and Doctors have a similar level of education to Teachers.
But these are flaws applied to the "fun" example, not the thing (blockchain + bitcoin) itself. Reading it might lead to a better understanding of the technology, but it is not a lot easier to read and understand than these, from Wikipedia:
As a classroom activity it might bring enlightenment, but, I fear, mostly enlightenment about the unworkability and complication of the scheme.
But let me add something about the two ideas themselves. Bitcoin has no intrinsic value. It's imputed value comes only from its scarcity and the expense (in cpu power) of creating new ones.
On the other hand, blockchain, is a distributed ledger that can keep track of anything using an anonymous and distributed system of agreement. It doesn't depend in any way on the difficulty or expense of creating a block, though it needs a scheme to prevent forging blocks. To be true to the idea the anti-forging scheme needs to be independent of any central authority.
For grades, neither of these, independently, seems to be very desirable (or necessary), unless we are in a post apocalyptic world (Road Warrior movie for example) in which there are no central authorities, having all been destroyed, and no centralized way to verify historical records.
However, a few words about bitcoin and similar things as they have worked out in the real world are in order.
Since it has become difficult to generate new bitcoin, two things have happened. Mining rigs are using up a significant amount of energy - and likely generating a significant amount of carbon dioxide. One estimate of the energy used is approximately that of the nation of Ireland. The other is that these rigs and the energy are expensive, so many internet attacks are now done to install bitcoin miners on other people's systems so that they can bear the cost without benefit.
The bitcoin market has also proven to be very volatile. Fortunes have been made (by the early investors/miners) and lost (those who believe the hype). That makes it remarkably similar to a Ponzi Scheme.