So my interpretation of how this works is that there's a server at api.iflix.io[1] which acts as (caching?) torrent client, and the browser just streams from that server. Seems like it probably won't last very long due to copyright issues, and/or will have very high bandwidth costs?

You can use it to download arbitrary torrent files by modifying the URL. For example, a changed link[2] downloads an Ubuntu ISO.

So there's no peer-to-peer work done by client-side javascript. (The server is written in NodeJS.)

[1] http://api.iflix.io/play/_SOME_MAGNET_HERE_/0

[2] http://api.iflix.io/play/b6b8ce579988a85b2a3ec8cd870ccb785d7...