And I couldn't find any way to just download them! It's not as easy as Vimeo where you can quickly steal the URL from the HTML5 player's
Lucky me, I'm stubborn. I disassembled the flash-based player, saw that it calls some ASP.NET web service through a SOAP interface and from that it gets an URL (www.hurl.it/hurls/0043f3b6d471…).
Lucky you, I put that same logic into a bookmarklet, so you can download whatever you want as MP4 files. Pretty nice huh!
So here's how you use it:
First, get the bookmarklet. Since deviantART won't let me put it here, you'll have to do a bit of extra effort. You need to create a bookmark, and use this as the "URL": pastebin.com/raw.php?i=fjfvzxA… (copy the text from that page and use it as URL, dA will mess up the code if I post it here as text because it converts some things to emotes).
If you don't understand this, go read about bookmarklets (Google it), it's very simple.
Now that you have it in your bookmarks bar/folder/menu, go to a screenr video page and click on the bookmarklet. A link will show up below the view count on the video's description, like this:
If it didn't work, or you're confused, read about what's a bookmarklet. It should work in all modern browsers, but I've only tested it on Google Chrome.
One caveat is that the filename will be random gibberish (a GUID/UUID), so rename it as appropriate. If I ever revise this I might fix that.
Hope you like it and good luck if it doesn't work, source code's here: gist.github.com/4699147.