Some of these have been touched on before but this is a more precise answer.
- First, panning. Like in the video, you can pan the guitars a little. If they're complimentary (i.e. playing the same melody and rhythm) then you can get away with more panning (as much as 90%) because they won't sound as imbalanced. If they're playing different things entirely then you can't pan as much. It's a harmony so you have a mix of both scenarios. I'd suggest you don't pan more than 30 if you want the listener to feel like the two parts are separate.
- Compression. I would never compress distorted guitars much at all since distortion has already done this for you (look how flat the waveform is compared with a non-compressed guitar). You can compress the peaks a little to keep things even though. Put a compressor on each and adjust the threshold so that it only affects the sound when it jumps up. Don't compress more than 3:1 (that's a ratio, assuming you know how to use a compressor. If you don't, google it, you'll find helpful explanations)
- EQ. The suggestion to add more highs to the more active guitar is an interesting one but I actually tend to do the opposite. Frankly you can do what you want in that respect but over all you need to create differences between the two guitars. The lowest one needs to have a dip at around 800 to 1000 hz, the highest will have a peak here. Then brighten one up at around 2000 to 3000 hz then the other at 3000 to 5000 hz. Adjust according to what sounds good to you.
- Reverb or delay. In my music I always use this to help distinguish sounds. If you want something to stick out, put less reverb/delay. If you want it to sound further away, add more reverb. In this case, add a light reverb (almost imperceptible) to the lower guitar then add a louder one to the higher up guitar (since this will soften the higher notes and make it more pleasant to listen to). The same goes for delay, less on the lower guitar.
- Other stuff. There are other effects you can add but I won't go into those now. This should give you enough to start with.