None of the free to play games on ps4 require psn to play online.
Why if we already bought this game isn't it free to play online?
Maybe ask Sony that question. My guess is the free to play games struck a deal with them.
I think the requirement to have psn to play online multiplayer and a lack of crossplay capability will be the down fall of cod and play station in general.
I myself will not buy another cod simply for this reason.. If i do i will buy a pc version.