Finish the main story. That is the way it has always been and that is the way it will always be. The other options are just wrong, if you speak to someone and say you finished a game it means you finished the last level or the end of the story, if you did everything in it then you say you beat it 100% and did all the optional things.
Most of the time I'm riding bicycles and on a lot of Colombian marching powder and coffee, forgive me if I act like an #%$hole. Or not, IDC.
Not every game has or needs an ending. It can be very hard to know what beating a game like Skyrim means when it's so open-ended and 98% of the content is optional, or downright impossible with arcade games which have no ending.
Good topic. As most of us remember, beating a game in the olden days meant killing the final boss (or something equivalent) and conquering the final level. That concept still remains true today. Optional objectives/side quests are optional for a reason. Once the credits roll; the game is finished.