However even if you wanted to move the file to a higher up folder in the folder tree, you had to use the move dialog to move the file, which takes a lot of time since there is no real folder "tree" along the left. However you do have a "bread crumb" bar along the top, which does tell you how deep you are getting in terms of folder levels.
One of the latest updates to SkyDrive you can now drag a file to a folder name in the bread crumb bar, and drop it. A picture is below to show you how it is done, and probably explains this better than I do:
The drag and drop feature works in both views, whether tiles (the one pictured) or the normal (what I usually use) list view.
Other features added to the latest SkyDrive update featured better display of sharing permissions, such as people who have permission to view and/or edit documents. Improved touch support for the tiles view was added as well.