You are wrong as far as assuming how jstorrent.com works. So I will elaborate a little on that first.
With jstorrent.com you are required to install it as a Chrome extension. Yes, it is only written in JavaScript. But as an extension it is no longer restricted to the sandbox environment it is in. It now has access to powerful APIs that allow it to access your filesystem and more. It also doesn't have the limitations that you would have with storage sizes and more. Additionally Chrome doesn't have a built in torrent client. These are implemented in the extensions. And jstorrent.com cannot possibly run at all as a regular website as a non extension.
JavaScript itself minus a few exploits in the past it is by far the safest browser scripting language available. Browsers intentionally try to lock it down and sandboxed as possible. Where things like ActiveX, Java applets, and Flash APIs are not completely sandboxed and a browser has limited control of them. But you can bypass this JS sandbox such as using a Chrome extension or using an application built with Electron which intentionally removes restrictions to allow expanded application development not possible through a regular web browser experience.
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.
Edit: It is worth mentioning there are a few solutions out there where an application runs on your machine and acts as the client. Using web sockets they can transmit that data to a torrent client front end coded only in JavaScript and no extensions required. However, it is important to know the sandbox at this point is bypassed with the installed agent and not the web browser.