Very interesting! And thanks for posting in Quicktime format.
Haier got slagged in one of the forums on That Home Site, but part of it was someone complaining that their compact washer was too splashy (that's not a bug, it's a feature!

. Seems to me all the Asian compacts are somewhat lightly built, but as with anything else, take care of it and it will last.
The units with the center-post agitators: these probably have a bag-style lint filter in the top of the center-post; if you don't have the user's manuals, see if it unscrews about 1/2-turn and pulls out. The lint bag needs to be cleaned out after every load.
The reversing motor / intermittent action agitator is the same action as used on the Danby twin tub. By the way, this will appear to be faster & a larger rotation arc when viewed in a computer video than it is in real life. That's an artifact of the video process.
The sound is different; the Haier sounds like a "wohh!" whereas the Danby sounds like a "whirr!" punctuated by the tick-tock of the reversing relay in the timer.
On the ones with pulsators, the little appendage hanging down in the tub is also a lint filter. This also needs to be cleaned regularly after every load.
The pulsator's moving tub is an interesting feature. I'm going to guess that the motion of the tub is deliberately lagged a half cycle behind the motion of the pulsator, to set up a counter-current in the water. The plastic ribs in the tub aid this process significantly. Very clever, and also probably reduces tangling compared to pulsator machines that don't have it.
The spin cycle appears to drain all the way before it starts to spin. Is that correct? Or does it start to spin when there is still some water in the tub? My guess is that if it drains completely, that's a feature to enable using a larger size inner tub relative to the outer tub.
Most interesting to me, it seems that the spin cycle in your first set of videos sounds as if the motor is switched on intermittently as the spin proceeds. That is, the video shows continuous motion, and the audio appears to have a continuous background noise, but the spin motor apparently sounds as if it's on intermittently. That feature probably saves a decent amount of power in the spin cycle. Very clever.
Question: How do these machines do with blue jeans? My impression is that denim is sufficiently stiff that you have to reduce the load size somewhat on the compact machines in order to accommodate jeans.
Re. ordering these things online: Try to find a place that's an appliance dealer with an actual store location, that also does online business. And more importantly, find one that's as close to you geographically as possible, to minimize the time the unit spends bumping around in a trailer truck. I got my Danby TT from Absolute Appliances in southern California; one day on the truck, and only a slight dent in the bottom front left which smoothed out completely via a little hand pressure applied from the inside of the cabinet. I think they also carry Haier.
In most cities and college towns, someone could probably earn decent money by setting up a small shop specializing in compact appliances, where people could come in & play with them on site, and either pick them up in person or have them delivered to their house or apartment. Danby, Haier, and a couple other Asian brands, plus whatever American compacts are still being made. Washers, dryers, dishwashers, fridges, microwaves, various countertop items, etc.
And of course there would have to be high-quality videos of the units going through their cycles. Danby has a compact dishwasher with a window in front, so you could even show a video of that one.
The sales angle would be "fits into your lifestyle" and "energy & water efficiency just got affordable." (Anyone here with some startup capital, want to start one of these in Oakland or Berkeley California, post here and we'll get in touch.)