So what happened to this site? Did people move onto something else (a site) or was it smartphones?
It was killed by Flash. Adobe is not just going to stop updating flash, they are outright force disabling it at the end of the year, even for people willing to risk it.
This kills the majority of the games on Kongregate.
And thus shockwave, with its .exe outputs wins in the end for old games?
Eh, you can still run a flash decompiler and recompile it to an exe (which embeds the flash player) https://github.com/jindrapetrik/jpexs-decompiler