If the resolution is set to 1280x720, OBS will only capture that specific area until told otherwise.
Set the video to 1920x1080 and then downscale it to 720p. Otherwise you will have to be running the game in window-mode and then capture the "window" itself for the 1280x720 to work properly.
There's also the option to "Fit to screen". Right-click your game and find it under "Position/Size" or shortcut CTRL-F :)