"Gauge" in this situation means the diameter of the wire carrying the current inside the cable. A heavier (thicker) wire has less resistance to current flow, so it has less impact on the signals in the cable - in this case, that results in better (maybe slightly louder) sound from the speakers. The longer a cable is, the more important it is to use a heavier wire. Wire Gauge is a number, and thicker wires have SMALLER numbers! And of course, thicker wires that use more copper are more expensive.
Speakers use relatively low voltages but higher currents than, say, simple audio signals like a microphone output to an amplifier, so using heavier wires for the heavier current on a speaker is a good idea. 20 gauge is thin for a speaker wire. 16 or 14 gauge is common. Some people will try for 12 or 10 gauge for speakers like this, but that's probably not needed for any reasonable cable length.
The triple cable system you linked to has three cables together running in parallel. Because that cable was designed for Composite Video and Stereo Audio signals, each of those three is a coaxial cable. That means it has one conductor is a flexible multi-stranded core in the middle, then some insulation around that, then a braided multi-stranded outer conductor sleeve that also acts as a shield to prevent outside electrical noise from reaching the inner central wire. Outside the shield is another insulating layer, which is the outside of the cable that you see. Such a cable, although intended for other uses, is just fine for a speaker wire also, as long as it is heavy enough for the higher current a speaker uses.
As I said, I could not find any specification for the actual gauge of the wires in the cable you linked to. My opinion that it is OK for this job is based on this: in the picture, I judge that the thickness of each of the three cables in the combined unit is close to the thickness of the metal centre pin sticking out of the RCA connector at the end. I know that size - RCA connectors are a standard size. In my experience, a coaxial cable of that diameter on the outside, or a larger one, contains inner conductors that are at least 16 gauge (maybe heavier) and suitable for speaker extension cord use if the extension is not more than 25 feet (7.5 metres).