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if Amazon can't make it one of their AWS offerings then it isn't true open sourceThat's because then it isn't. Sorry, but you can't just take terms with an accepted meaning and decide they mean something else, without any conversation or consensus from there people using that term.
The OSI has a specific definition of what "open source" means[0]. Restricting what users of the software can do in this way is in direct opposition to parts of that definition, so no, if you do that, then it is no longer open source.
I'm not saying you aren't entitled to set up your licensing that way. I think it's disgusting when the likes of Amazon decide to take someone's hard work and use their massive oligopolist position to trivially outcompete anything the original author might try to do to make some money.
But that doesn't mean it's open source. I think people need to stop being so afraid to call their software something else. They seem to be really attached to the idea of being an "open source developer", and don't want to drop that moniker even after changing their licensing away from open source.
People also need to stop licensing their software under true OSS licenses, building a community of regular, significant contributors around it, and then changing their licensing (which they can do because they've [IMO shadily] required contributors to reassign copyright). That's a huge bait-and-switch, and people are right to be upset when that happens.
In the case of Bearblog, it seems like the author is really the only significant contributor, so I think what he's doing is totally fine, for the record. Frankly I think he did this the right way: his announcement email is entirely reasonable and sympathetic, and he doesn't try to breathlessly claim that his software is still open source.
[0] https://opensource.org/osd [1]
[1] While I don't love how the OSI folks basically just decided they own the term "open source" and that they get to define it, I think they've been pretty good stewards over time, and having clear-cut definitions of things is a good thing.