Runners play and complete the story mode from the beginning to the real ending (How to Make your Game!), using any route they wish. The ingame (Story Mode) timer will be used.
There is an Auto Splitter for LiveSplit that reads accurate ingame time from the game, and it is strongly recommended that you use it. If you don't use accurate Game Time or if you can't make the timer visible in your video, you have to enter the stats screen from the main menu after your run, and your time will be the time shown + one second. This is because the time displayed in the stats screen is always rounded down.