To put any game or application on another PC you would have to install it --- it won't run simply by copying files across.
some games do have "self installation" like LoL, WoW, WoT, you can copy the files and play normally no need to "classic" install. but i think this question was more of a can we both play at the same time on internet with a single copy of the game ( due to being BO4). like a "yaaaaarrrrrrrrrr" question.