Mine's a 2013 vintage Les Paul Studio model, so that makes your guitar about three years younger than mine, I think the silver shields on my guitar's pickups do something to the midrange frequencies cause when I played it through my Marshall amp, the tone was very midrangey, fortunately it's a tone that I really like.
That Les Paul in the video clip is a nice one, the bridge pickup sounded like it wasn't adjusted properly with respect to the strings, or it could have just been due to how youtube handles audio.