The 1.11 version of the Mission Editor is located in the Installation Path\Dawn of War\ root folder. To run it, use the start menu shortcut or create a new one pointing to the W40kME.exe file in the root directory.
Previous versions required you to set the location of the W40k.exe file – but this is now not the case. You can run the executable directly.
When the ME loads, there will first appear a Debug Screen, and after that (if there are no display errors) it will open up the mission editor window itself. If nothing appears, try using ALT + TAB to cycle through programs until it appears.
Mission Editor