All right. The solution is here. I was so stupid. Stupid, stupid, stupid... Here are the steps. Some of them may be skipped, further testing is needed. International language pack files to follow.
1) Copy en.sb and en.toc files from the international version to the "C:\Program Files (x86)\Electronic Arts\Dragon Age Inquisition\Data\Win32\loctext" directory. You don't need to delete the "ru" files.
2) Copy GDFBinary_en_US.dll from the international version to the "C:\Program Files (x86)\Electronic Arts\Dragon Age Inquisition\__Installer" directory. You do not need to delete GDFBinary_ru_RU.dll.
3) Open the registry editor, go to "HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\BioWare\Dragon Age Inquisition", and change the following keys:
Locale: from "ru_RU" to "en_US".
GDFBinary: from "C:\Program Files (x86)\Electronic Arts\Dragon Age Inquisition\__Installer\GDFBinary_ru_RU.dll" to "C:\Program Files (x86)\Electronic Arts\Dragon Age Inquisition\__Installer\GDFBinary_en_US.dll".
4) Now go to the "HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Origin Games" key. There will be a bunch of subkeys related to Dragon Age Inquisition. Change the "Locale" to "en_US" for all of them.
5) Download Outcome - free replacement for the Origin client: http://outcome.nofate.me/
6) CLOSE ORIGIN!!! (this was my mistake). Run Outcome, log in with your origin credentials, and let it patch the DragonAgeInquisition.par file.
7) Run the game directly (DragonAgeInquisition.exe) or using a desktop shortcut. Enjoy the full international version 
Please confirm that it's working for you.