Using "vanilla" to describe a standard, unmodified and un-customized version of something is a very common idiom. This satirical website followed the convention, it didn't coin the expression. I don't think it's even jargon, it's just based on the meaning of the adjective "vanilla":
Lacking adornments or special features; basic or ordinary: "a delicious twist to a vanilla plot" (Ian O'Connor).
For "vanilla js," I can still have compilers, type checking, advanced ECMAScript 2019 features, local storage, webgl, etc. Without that understanding, you could qualify something as "vanilla js" in lots of different ways.
If someone said "vanilla c++," they might mean c++ without the recent language features, or they could mean the latest language spec but no standard library. Maybe it's still okay to link OpenGL but not okay to use a desktop GUI framework? Maybe OS frameworks are okay but nothing more? There's no communal understanding there that I'm aware of.
I personally don't think there's a market for non-js users. Most of the web is pretty broken without. I've never encountered someone in the real world who lives this way, even in the tech world. At most, someone will install a no-script browser plugin. That makes whitelisting and enabling javascript dead easy for the user. The only legitimate non-js use cases, IMHO, are for extreme political cases where you'd also be using TOR.