I can't speak for Deezer, but there are several new APIs in development for HTML5 including the FileSystem and FileWriter API.
In use cases it gives examples of large storage requirements the API will be able to fulfil such as storage of large media files and assets.
Offline video viewer
- It downloads large files (>1GB) for later viewing.
- It needs efficient seek + streaming.
- It must be able to hand a URL to the video tag.
- It should enable access to partly-downloaded files e.g. to let you watch the first episode of the DVD even if your download didn't complete before you got on the plane.
- It should be able to pull a single episode out of the middle of a download and give just that to the video tag.
It's still a working draft and not very widely adopted.