An air conditioner is not, in fact, more efficient in a low thermal mass house than a high-thermal-mass house.
In fact, adding thermal mass, everything else held equal, usually makes the air conditioner more efficient.
The article you refer to is engaging in "bench-marketing", picking tests that seem to show their product is better while not mentioning other tests that seem to show their product is not better.
If I were a manufacturer of one kind of air conditioner, I would be tempted to try to attract people's attention to situations where my air conditioner is better than my competitor's air conditioner, no matter how unrealistic those situations may be.
In the summertime, I want my house to stay at a nice constant 75 F (297 K), even when the temperature outside is over 100 F (311 K).
Heat energy from outdoors inevitably leaks into my house one way or another.
Also heat energy from human bodies, computers, soldering irons, hot-glue guns, etc. also gets into the interior of my house
The purpose of the air conditioner is to maintain a comfortable temperature,
which it does by pumping all of that that heat energy to the outdoors.
(One could argue that my air conditioner is merely "maintaining a constant temperature" and therefore I'm "not using it for cooling" to a lower temperature.)
Because the thermal mass inside the house is staying very close to a constant temperature, no net heat energy is flowing into or out of that thermal mass.
So in theory the air conditioner shouldn't even notice the difference -- an air conditioner would continue pumping heat energy at the same rate, using about the same amount of electric power -- if I double or halve the thermal mass inside my house.
In practice, however, the amount of thermal mass does have a small effect on the amount of energy used by air conditioners.
Two kinds of air conditioners
Some air conditioners are "bang-bang" "on-off" air conditioners that either run at full speed or turn completely off.
Some air conditioners are "variable speed" air conditioners that more-or-less continuously run their motors, smoothly changing their speed in response to current conditions.
All on-off air conditioners use energy to spin up the motor every time they turn it on, and practically all on-off air conditioners do not recover that energy (the energy is lost) when they turn the motor off.
Variable-speed air conditioners (sometimes called "inverter air conditioners") run more-or-less continuously, so they don't have the same kinds of losses.
At any given instant, heat energy flows into my house at some rate (heat leaking through the walls and windows, chemical potential energy being converted to heat energy, etc.).
Assuming the interior temperature is already close to the setpoint
(which it almost always is), a variable-speed air conditioner attempts to pump heat energy out of the house at exactly the same rate at every instant.
In principle, we could attach a on-off air conditioner to a small, leaky box and push the setpoints so close together than it would try to turn on-and-off the motors once a second -- that would be horribly inefficient.
Every time you double the thermal mass, that would make the bang-bang air conditioner turn on and off half as often per day,
halving the amount of energy wasted on starting-and-stopping the motors.
In practice, bang-bang air conditioners run for a long time, and then stay off for a long time, so the amount of energy lost starting-and-stopping the motors is small relative to the amount of energy used to keep me comfortable.
(The total energy used by an on-off air conditioner also includes the unavoidable energy that Carnot calculated is required to pump heat energy, and also various other inefficiencies, so doubling the thermal mass won't halve my electricity bill -- it only halves that relatively small amount of energy lost starting-and-stopping the motors).
If you attached a variable-speed air conditioner to such a small box,
it would have to rapidly change the speed of its motor every time the flow of heat changed.
But that would probably take much less energy than starting-and-stopping the motors of an on-off air conditioner.
If you doubled the thermal mass, then the variable-speed air conditioner could take twice as long to ramp up the speed and still keep the temperature in the comfortable zone; slower changes in speed require slightly less energy than fast changes.
(The total energy used by a variable-speed air conditioner also includes the unavoidable energy that Carnot calculated is required to pump energy, and also various other inefficiencies).
If our goal is to keep the house at a comfortable temperature,
adding thermal mass makes both kinds of the air conditioner more efficient.
In the "unrealistic conditions", the on-off air conditioner is horribly inefficient and so the other kind of air conditioner looks vastly superior.
In more realistic conditions, the superiority of either one over the other not at all obvious.
(Why am I posting an answer to my own question?
Because it is "explicitly encouraged" by an article linked to in our FAQ.
Does this mean I think my answer is the One True Answer?
No. In fact, this answer is jaded and cynical, and I'm kind of hoping some other answer will bring up some point I'm overlooking.)