Also, Helium is an escape artist, extra thought must be given to your design to prevent leaks.
I'm also wondering how heat is moved in to the unit, and out of the unit. Since normal heat pumps gain a lot from doing the compression/evaporation right where the heating/cooling is needed, but what I get from the article is that this focuses on heating water.
As for moving the heat, since it's using water as a heat medium, it just moves the water to the hot or cold spot on the internal stack to heat or cool as appropriate.
Doesn’t that produce perpetual motion, given a cold reservoir?
The downside is probably cost of manufacturing. Ben & Jerry's prototyped thermoacoustic cooling in 2004 [1], but now their "Cleaner Greener Freezers" are refrigerant based, although they're using a hydrocarbon refrigerant rather than a traditional hydrofluorocarbon. I'm not sure which specific refrigerant they're using, but based on the timing, it might be R441a, which was the first hydrocarbon refrigerant approved for sale in the US and is a mixture of ethane, propane, butane and isobutane. [3]
[1] https://www.npr.org/2004/04/28/1861434/ben-jerrys-uses-sound...
[2] https://www.benjerry.com/values/how-we-do-business/cleaner-g...
[3] https://www.acr-news.com/hydrocarbon-refrigerant-r441a-gets-...
For heat energy the quality is related to temperature. And is basically the percentage of it that can be converted to 'work'. For electricity the quality is near 100%.
So a heat pump moves low quality heat energy inside you house say at 65 degrees and dumps outside where it's say 90 degrees. The energy you move needs to increase in the amount of quality. The increase in energy comes from the electricity used to drive the pump.
The trick here is that the COP of both isn't static, but is usually a peak. Heat engines are more efficient the higher the temperature difference, while heat pumps are more efficient the smaller the difference. For any given heat gradient, you can't have a total efficiency of a heat pump + heat engine that exceeds 100%.
This heat pump will also have to move the heat energy from somewhere. It can't do that if there's none to begin with.
A 1kw heat pump providing 4kw heat is pumping 3kw heat from outside. Similarly it could be providing 4kw of cooling by pumping in reverse. Most heat pumps are reversible.