I'm going to ignore the piracy aspect of this site (since I don't support copyright infringement) and just talk about the implementation. This site is connecting to a centralized service to fetch the torrent data. It's not P2P, it's easy to censor, and it likely won't be around for long.
What we really need is a true P2P implementation of BitTorrent in the browser. I'm working on just such a project: WebTorrent (http://webtorrent.io).
You can see a demo here: https://instant.io
Here is a link to watch Sintel (Creative Commons 3.0): https://instant.io/#c6642b73cf82dc52b5d538fabfdf9c8e3d9e850f
WebTorrent is powered by WebRTC, the de-facto standard for connecting two peers in the web browser. It even works in desktop apps (via Electron or NW.js) and mobile apps (via embedding the webrtc.org library).
With WebRTC, we can connect all types of endpoints (desktop, web, mobile) directly and completely P2P. This is the underlying transport that all future P2P protocols should be built upon.
Right now, the primary limitation of WebTorrent in the browser is that you can't just paste in any random magnet uri or .torrent file and have it work. The torrent must be seeded by a WebRTC-capable client, i.e. webtorrent-hybrid (https://github.com/feross/webtorrent-hybrid) or https://instant.io.
We plan to build a desktop client (soon!) that can connect to normal BitTorrent peers, as well as WebRTC peers. These long-running peers will ensure there's lots of content available in the network that the shorter-running web peers can access.
This is the vision: All torrent clients (desktop, web, mobile) talking directly to each other. If you're interested in learning more about the idea of "WebRTC everywhere", here are some links: