Confusion with voltage rating when sizing wire gauges
Voltage rating applies to the insulation, but there are subtleties.

On very low voltage (like 12V), pretty much any insulation thick enough to stick to the wire will do. On higher voltages, insulation thickness and material type really matters. 

For example, the wire you link is a hookup wire for low voltage  electronics. In this use case, you want thin insulation, because this makes the wire more flexible, and practical to use. This explains the very low 60V rating. It will be inadequate for your 80 volts. 

If the wire is exposed (for example, it runs on the floor and people could walk on it) or if it is exposed to vibrations or chemicals, then of course this has to be taken into account too. Insulation will need to be rated for this.

In your use case, I would use simple 2-conductor lamp cord. It is cheap, readily available, inconspicuous, and robust.

EDIT: 

For a 20m run it will most likely be mounted on walls or at least attached to something, so check regulations in your area for things like   electrical conduits, etc.

For example, your hookup wire would only be allowed inside an enclosure. Here, as a general rule, wires with hazardous voltage are not allowed to be apparent, which means they have to be inside a conduit, for example:



If it can be touched, walked on, etc, then it has to be a cable. In the above photo, if the wires were cables instead, the T-junction could be omitted, with cables visible. In this case, the conduits would be used more as a convenient way to bunch up the cables and mount them on the wall.