“Sidechain” is a few different things depending on context. First (and the way EHX is using it in the manual) the “sidechain” is the part of the signal path of a compressor that “triggers” gain reduction. When one sets the threshold level of a compressor (the level over which the compressor starts turning stuff down), the signal the compressor actually looks at to see if it is over the threshold is the “sidechain”.
In many compressors, this sidechain is the same thing as (or is derived from) the main input signal. So if you feed it drums with loud bits and soft bits, the loud bits will trigger the compressor which will make them soft.
Some compressors, however, let you specify the sidechain signal independently. So you could feed it drums on the main channel, but give it, say, vocal narration on the sidechain. Now the compressor doesn’t care what bits of the drums are loud and which bits are soft. It only cares about the levels of the narration — it makes all of the drums quieter when someone is speaking (this particular setup is usually called “ducking”).
So now, the kind of techno pumping “sidechain” you’re talking about is a specific effect achieved by putting everything but your kicks through the main input of the compressor but triggering compression only with your kicks by routing only the kicks to the sidechain. The as a result, the compressor doesn’t care at all about the loud bits or soft bits of what you’re sending through main. It just makes it quieter whenever the kick hits. This “ducks” the non-kick content leaving the kick untouched and making room for it in the mix. Depending on the release settings of the comp, it can also make a pumping effect that is sometimes desired and sometimes not.
This is not how the EHX operates. You essentially have no control over the sidechain. It just takes the main (stereo) signal, sums it to a mono signal, and uses that to trigger compression. The only reason “sidechain” is even mentioned is to make clear that the pedal doesn’t output mono — that the mono signal it sums is only used to control the compressor.
So what’s the big deal? If you have a mix with a bunch of stuff and a really loud kick on top, and use all that to trigger the compressor, won’t it still (depending on threshold) make just the parts with the loud kick quieter? Yes, but with one big difference — because the kick is part of the mix, it’ll make all of it quieter, proportionally. So if you have a bass in there that’s muddying up your kick, it’ll still be there, and still muddy. If you can sidechain your kick, you can squash everything under it while leaving the kick untouched, “making room” for it in the mix and giving it much more impact as a result.