Critical issue with this technology it only really works well with helium.
Reading up a bit, it seems like this has to be a traveling-wave device to get the efficiency advertised: standing wave devices seem limited to a Carnot cycle, where a traveling wave device can operate a Stirling cycle.
Since most of the worlds natural gas is in Qatar and Iran, the world will just have a helium resource crunch if this becomes widespread. Maybe a better working gas to use would be ammonia or desiccated propane.
Maybe the ultimate solution is to have neighbourhood heating/cooling units that serve multiple and pipe hot/cold water to them.
hydrogen is actually even better iirc
but air works too
but 2 ℓ of hydrogen (i don't know how much you'd use in a residential thermoacoustic cooler so that is a guess but probably the right order of magnitude) is only 0.02 megajoules, a thousand times smaller
otoh the kerosene doesn't form an easily detonated high explosive if it mixes with air, and the hydrogen does, and 20 kilojoules can still be plenty fatal in an explosion