It CAN be complex in terms of the number of things you have to keep track of for the story to make sense, so it can be something completely insignificant like a character just mentioning or wearing something different, in which case yes, just a variable is all that's needed, or it can be indeed, something quite complex like completely different branches of story that can have several repercussions depending on which and how many choices are involved.
I don't know how complex this game's update actually is thou, I'll wait until I download it and see the assets in it to form some judgment on the matter.