1) Install wine (yes I think wines ubuntu ppa installs files that makes cryengine happier - weird, try without wine if you want - or just try wine by itself).
2)Create a new bottle, call it what you want.
3) Put the CryEngines files from the zip into a new folder within the bottle (I chose drive_c to avoid spaces in names).
4) In the bottle, install the Visual Studio C++ 2008 Redistributrable.
5) In the config, add the CryDevLogin.exe as a new application.
6) Highlight the new application, go to Libraries and set an override for mfc90.dll to native.
7) Launch the editor or launcher, login as usual.
A couple of points:
1) The Editor is very slow to launch (so much so you won't think anything is happening after double clicking the exe icon).
2) It's normal to get a complaint about an unsupported video vendor
3) Changing/Disabling the skin with a map loaded crashed the editor for me, but worked fine with just the editor loaded and no map.
4) The Launchers main menu UI is a bit garbled, but is useable.