The description given is for elementary backstroke which is a gliding and survival stroke. I don’t remember if I was taught with these words or if I used them long ago when teaching the stroke but they are descriptive. In the old Red Cross swimming levels in Advanced Beginners this was one of the strokes taught. I think it was taught before back crawl (backstroke shown in #11) which everyone that swims competitively calls backstroke.
Elementary backstroke has easier arm strokes since the recovery is in the water. The stroke uses the breaststroke kick on your back. Learning the kick is easier and you can breath on your back. It was quicker to learn breaststroke because the swimmer already knew how to do the kick so just needed to learn the breaststroke arms.
Elementary backstroke with good kick and the finish of the stroke to your thighs you could glide for a few seconds before stroking again allowing for a rest. You actually go faster if you take a glide.
I think the memory mnemonics I used when teaching was start with your hands at your side, touching your legs, then pull the zippers up to your armpits, straight out to a T, then push straight to your legs. Kick moves/ synchronizes with the arms which is a little different than breaststroke on the timing of the arms and kick. (Shorthand was up, out, together while demoing the motions.)
This is really good video if you want to learn the elementary backstroke.