I used to love Flash games, and I was also watching the projects that tried to get .swf files to run in a Flash virtual machine emulated via something like Emscripten, but I feel like all those projects have died out :/

And Flash for animation: e.g. this was produced and published in Flash and was surely smaller to download than the youtube video of it:

https://www.youtube.com/watch?v=LeKX2bNP7QM

The internet speeds were much slower then, the difference mattered a lot. Also note, from the description:

"Sadly, it's not possible to replicate the pop-up mouse-overs from the "Special Edition" - though I was able to append the "deleted scene" presented in that version. If you want to see that version - or the "Fire BAD!" flash video game where you attempt to extinguish flames on James Hetfield (tragedy + time = humor), you'll have to find the original .SWF files and have a way to play them."

In that regard, looks like Unity is the new Flash.

It is and it isn't. Unity is great but it's got like a min 5MB download for just a spinning cube. Flash (because the plugin was built in) started instantly and had built in support for streaming. Unity can stream, after the 5MB engine download, but for whatever reason it's not common.

I meant more as in people with no technical knowledge whatsoever creating interactive stuff. Just look at the cambrian explosion of indie games from (most) people who probably can't do long division by hand.

Very likely! But some years ago, back when I still played Flash browser games, Unity games didn't work in a browser for Linux, the only platform I use. Maybe that situation has changed? :)

What with a WebGL target for Unity these days, it has. The Unity plugin was deprecated versions ago and they don't even ship a target for it anymore.