I was finally able to find out the solution browsing these forums. In a thread started as far back as in 2009 a user posted this command that happens to be the correct and ultimate one.
sudo /System/Library/CoreServices/Language\ Chooser.app/Contents/MacOS/Language\ Chooser
It will initiate language selection tool, the one that appears at the initial steps of setting up OS X right after it has been installed and invokes GUI window with all the available languages, including the one I needed. Once you choose it and hit Return, this language gets assigned system-wide including other user account on your Mac. Though clever, it's certainly not that simple as Apple declares it to be, and not user-friendly, not speaking of installation glitches causing such mess.