When there is no wind then they DO retain heat indirectly by significantly lowering the amount of evaporation (see
this post that shows that 1/4" of evaporation will lower a 4.5 foot average pool depth temp by 4.9ºF). About half a pool's heat loss comes from evaporation of the water, NOT from conduction or radiation. So these liquid pool covers DO work IF there is no wind. However, that's a big "if". With wind, the single molecule layer tends to get pushed to the side exposing water to be evaporated.
A bubble-type cover is obviously a lot better, not just because it is not affected by wind, but also that it not only prevents evaporation, but has air bubble insulation that significantly reduces conduction. Whereas a thin non-insulating cover and perhaps these liquid solar covers with no wind may cut down heat loss in half, the bubble-type cover cuts down that remaining loss in half again. So if one were to lose 6ºF overnight with no cover, a thin or liquid cover may cut the loss down to 3ºF while a bubble-type cover would cut it down to only 1.5ºF. These covers also work during the day, but then in addition to heat losses there is heat gain from the sun heating the water in the pool. Very roughly speaking, you can expect a bubble-type cover to raise pool temperature above the average day/night about twice as much as a thin or liquid cover. So instead of a 10-15ºF increase, you may only get a 5-7ºF increase.
I have an automatic electric safety cover and it is relatively thin and not very insulating so in my pool I only get a roughly 50% reduction in heat loss due to preventing evaporation. If I were to use a bubble-type cover, I'd retain more heat, but it wouldn't be automatic. Since I have a solar system to heat the pool, it nets out OK for the convenience of an automatic cover.
As for the "1" for health which means a SLIGHT health risk, that is referring to the CONCENTRATED chemical. The 1,2-Propanediol will evaporate (it's just used as a carrier for dispersion), but the 1-Octadeconal (aka Stearyl alcohol) that remains has an LD50 better than table salt. Most certainly when diluted as a thin one molecule layer on the water, it will not be hazardous even if your dog drinks from the water.