> The kind of "open source" I was talking about is source code that is released under a non-free software license. What do we call that?

"obnoxious".

More seriously, typically something like "look but don't touch", or "proprietary with source available", or "source available under a restrictive license". Microsoft used to call it "shared source", and that term still has those connotations too.

Definitely not "open source", though; that means more than just "has source available".

It's common practice in the game industry to license/pay for access to the source code. Whether you end up changing it or not is up to you, but at least you have a choice. This might not be true for Microsoft's "public" source code. I don't know. It looks like we're talking about two very different domains.

The Unreal Engine is an example for this kind of business model on a large scale. KoboldTouch (used to be?) an example for the same on a very, very small scale (less than 5 people). I really don't see anything "obnoxious" about it.

> It's common practice in the game industry to license/pay for access to the source code. Whether you end up changing it or not is up to you, but at least you have a choice. This might not be true for Microsoft's "public" source code. I don't know. It looks like we're talking about two very different domains.

Yeah, that's a very different case. It's indeed moderately common for proprietary software frameworks/engines to include source, so that their paying customers can modify and redistribute, but cannot redistribute in source form (modified or otherwise). That's not any more obnoxious than any other kind of proprietary software distribution, and I wouldn't call it "look but don't touch", though it certainly isn't open source or free software.

The case I'm talking about is software with publically available source, but under a restrictive license that doesn't satisfy the OSI or FSF or DFSG definitions. For instance, many random projects on github that don't bother applying a license, or rar (the archive format implementation), or tarsnap, or the extremely obnoxious JSON license.

There's nothing wrong with doing that. Feel free to do whatever you want. But what you are talking about is not "Open Source". That term has a (different) meaning. If use "open source" for that, you will confused and trick people.

"open source" has been in use as a term in tech for a long time. It means (essentially) the same thing as "free software". Licences that disallow derivations (or commerical derivations) would not fall under the defintion of "open source" that nearly everyone uses.

You are free to come up with your own defintion of popular, agreed up terms. But this will lead to problems when you're using a different definition from everyone else.