In what sense do you believe that it is not a blockchain? Because I would say that Git is an extremely compelling use case that satisfies all the criteria in that flow chart.
Blockchains get their history rewritten all the time too, it's call a re-organisation and occurs naturally whenever two blocks are found close enough together that the network splits over which one came first. You can also get longer rewrites of history when there's a bug or an explicit decision to fork the chain.
The idea that blockchains are 'tamperproof' or can't be changed isn't really true. At most you can say that participants can become aware of such changes. But that's also true of git.
That said, there are a lot of good uses for the tech as long as "the tech" is understood widely. If you look at the enterprise blockchain space they're moving away from classical proof of work type systems, they all use BFT algorithms instead, and some of them don't have blocks at all (like Corda). They're more git-like and they provide most of the advantages but without the disadvantages; which can indeed be very useful for many types of business.
I wouldn’t call it blockchain though.