First patched Steam version to 1.0.0.8 it asked activation code, like I guess it's was supposed to do. Didn't see any trouble with the game, however decided to download and put EDs original version, so uninstalled Steam version completely, installed version 1.0.0.7 and then patch 1.0.0.8 - Started game and it didn't even ask activation code again. All works well and no Steam in background when playing game.
Alt-tab didn't work on Steam nor any community things, I guess reason is the 64bitness. No reason to keep Steam version installed when you can download the game from EDs site. Also possible future installations are quite nice if you already have the install package in HD.