The GECK/creation kit.
Every Bethesda game uses cells in its outdoor areas. By measuring them, since their sizes are given, you can find the total playable area easily.
-Morrowind was 10 square miles.
-Oblivion was 22 square miles total, but only around 16 of that was playable due to the rest being outside the invisible wall, since they had to map parts of all the nearby provinces for the player to see once they reach the end of the game world.
-Fallout 3 was also 16 square miles.
-Skyrim was 14 square miles.
Further complicating the issue about Fallout 4's size is that the map shown in the video you posted isn't the whole map. According to the map extracted from the pipboy app data, the glowing sea extends BEYOND the dashed border. There is a fairly substantial part of the map seemingly outside the dashed border.
On top of that, the guy who ran from one corner of the map to the other only ran on the land area IIRC, meaning he didn't count all the water from in the lower right hand corner when doing map size. Further throwing the total size off.