No, you're not missing anything. The Live Desktop is a "place" and perhaps you could say it mimics the desktop, but it isn't a cloud based application suite. It's simply a storage location with some extra functionality. The future may bring much more functionality, perhaps from 3rd parties even, to the platform, but for now the Live Desktop is simply a convenient web access point to the data you are synchronizing between devices.
Word is that we'll see the services of Live Mesh, Live Sync and SkyDrive somehow merge moving forward, so perhaps we'll see some better representation of the files in the space due to this.
In the meantime, if you want to submit your suggestions/expectations, you can do so on Connect per the instructions here:
Live Mesh Beta: Suggestions - Go cast your vote!-steve
Microsoft MVP Windows Live / Windows Live OneCare, Live Mesh, & MS Security Essentials Forums Moderator