You just have to make sure you don't have the EUI two times:
Cut-Paste the EUI folder (Asset/DLC/ui_bc1) elsewhere. Launch civ and go to the "settup game". You will immediatly see if the EUI is enabled, since the "feature" of being able to se the description of unique units in the settup is an EUI feature.
=> If the EUI is enabled, it means you had it two times, so you can play.
=> If the EUI is disabled, it meands you had it only once, so you have to quit, add back the EUI folder, and launch again.
Alternative methods is to search in the DLC folder and your modpack folder (and subfolder) if there is a second copy of the "ui_bc1" folder