If certain conditions are met, then yes it becomes funcoms responsibility, the mod would have to be in the workshop “and” funcom would have to be aware of it.

For example, workshop mods are considered an extension of the game and keep players active which increases the games popularity and results in funcom making money, if they are aware of a mod that is doing something illegal and do nothing about it they themselves become liable as they are profiting from it.

This only applies to mods added to steams workshop, also if steam becomes aware of it they also become liable hence they tend to take a heavy handed approach to copywrite disputes, I believe this is also the reason why funcom (or anyone) wouldn’t contact the author prior to taking the mod down.