Sound quality on that vid makes it hard to pick things out. The sound reminded me of a cross between The Greatful Dead and the The Allman Brothers. I've never been a fan of the Dead, but I love the tones Dicky, Duane, and Warren got with the Allman Bros. Frankily, I didn't really like the Les Paul tone on that vid. It sounded like it was run through a notch filter of sorts. It's a familiar sound that works for others, but not me. I prefer a more traditional Marshall "Plexi" tone, or JMP, or JCM 800, etc.
I'm still playing around with my Les Paul tones on my new 18 watt head. With the various overdrives I have, I have a lot of options. Straight in, the amp sounds great. It's a bit saggy, and not as aggressively focused as a solid state rectified Marshall. I have 3 different overdrives that I use to color my tone to different flavors:
Marshall Guv'nor (original UK-made Black box): I use this for a Marshally mid-range grind. Invokes a fairly aggressive JCM 800 type of sound.
Analogman Beano Boost: This thing colors my sound heavily. It works well for Jimmy Page / Zeppelin sounds. Really throaty, honky sound, no matter what mode it's in. I usually leave it on treble boost. I haven't tried it with batteries yet; but as I suspected, it doesn't seem to like my Voodo Labs PP II power supply much. I have to dial the sag control all the way down to 4 volts to reduce all the noise. I suppose I should try a battery.
Crowther Hotcake: I just love this pedal. It is a great lead boost pedal and adds a nice aggressive upper end presence and grind to the tone. Really makes the sound more full and round. It just seems to take the original signal and make it sound much better in general. It doesn't color the tone as much as the other 2 I noted, but it still does in a good way.
Foxrox Octron: Usually used for single-note runs. I found some really cool sounds when I just barely dial in octave up and down with a full direct signal. It makes a full barred chord just bloom with added harmonics and depth. It's really easy to over do it used in this way.
Anyway, I'm babbling. Just some of the sounds I experiment with.