A screenshot is an image,and the copyright in an image is vested in the person who created it. That person would simply have copyright in the image itself - nothing to do with the game,unless by publishing the image the copyright holder infringed the intellectual property rights of the game's producer.
Modifying a game's content may be a permitted action according to the software's EULA, and there's nothing to prevent someone making a screenshot of the modification - it would again be a case of copyright in the image being vested in its creator. As long as the image wasn't used to infer any intellectual property right in the software itself there would be no problem.
The EULA relates to the use of the software itself, and doesn't prevent anyone from making screenshots. To be on the safe side, I would advise that any publication of the image itself should be accompanied by an acknowledgement of the game company's rights in the software, and of any trademark if a registered trademark exists.