When you are using cockpit view what you see is the same as if you were actually in the vehicle. Of course when running the Sim you see your monitor or monitors, if you are using triple monitor setup but you don't really notice them as your focused on the track . When you capture game footage though it will show what you are seeing in this video, only the track, other cars etc . You will sometimes see videos posted where the poster is using a camera setup behind them which will show the Sim rig , the monitors the player/driver and everything in the cameras view . This one above is " in game " capture using the record/capture function built into the game engine.
If you go to about the 9 minute mark of this one it shows the difference as he is using split screen in his video. The top half is captured in game so all you see is the track. If you look at the bottom left you will see him and just the corner of his monitor because of the ange of his " external " camera ,