I realize this response is one year late, nevertheless I found a fix for this issue in another thread within twcenter.
The fix is related to Steam. I assume you are using Steam to run the game?
Follow these steps and your game should work:
1. Follow Itan's instructions for installing the mod. The instructions are as follows:
[Sourced from Itan's mod installation instructions]Run my program "Empire Total War.exe", choose the language game, select the campaign to play, start ModManager and uncheck on "show all pack types" and "show vanilla conflicts" so to display only files .packs that interest us, to enable all the mods (the ones with the prefix IT_) and then clik on "LAUNCH". Now the empire is set next time just click on "PLAY" and the game will start with the mod enabled.
2. Problem is here: "then clik on "LAUNCH"" - don't click 'launch'
3. Once you select your game settings, and
4. Follow appropriate steps for Mod Manager
5. Save settings in Mod Manager and click the 'X' - close option for the window. *** This is the important step.
6. Open your Steam app
7. Find your Empire Total War Game,
8. Run/Launch Empire Total War through Steam
9. Your game will work with Itan's Mod
Therefore: the problem is with Steam. If the fact is that your game is a product installed through Steam, you must run/launch the game via Steam in order to avoid the 'Application Launch Error'