You are wrong as far as assuming how jstorrent.com works. So I will elaborate a little on that first.
So could another browser support a JS torrent client? If they have an extension system or allow mods to bypass sandbox restrictions then absolutely. Firefox has a torrent client extension as well.
However both have separate APIs and separate ways of doing things. You would be looking at a lot of work to get jstorrent.com on Firefox or another browser.
So in closing, Chrome is not doing anything out of the box to risk your security. You are as soon as you are opting in to install an extension with elevated privileges. And yes, a torrent client could be made in the same way for any browser that has an extension system with the desired APIs available.