NE5532 has 100dB voltage gain at DC, so with shorted IN+ and IN- pins a mere 0.013mV difference in input offset voltage is enough to produce 1.3V output difference. As the outputs are shorted too, this drops 650mV across one output resistor of each opamp and overcurrent protection is activated in one of them (which one limits first depends on part-to-part variation and whether the sourcing or sinking current limit is lower, as they are unlikely to be exactly equal).
Let's start with the obvious: the chips run hot and they may overheat and die over the long term if supply voltage is too high. Power is voltage times current, do the math. You probably shouldn't exceed 0.5~1W because a pair of hot chips stuck together may dissipate not a lot more heat than one alone.
A more interesting question is how and why the amplifier ends up working anyway. Under no load, the "weaker" side which runs into overcurrent limit first is simply a constant current source, while the "stronger" side gets biased in its linear region and drives the output in class A. So far so good.
But assume that one chip sources constant 38mA and the other can sink up to 40mA. When the load demands more than 2mA to be sunk, the sinking chip runs into current limiting too and loses control of the output. Then the differential input voltage needs to move the difference between offset voltages of the two opamps before the sourcing one desaturates and starts to reduce its output current below 38mA, allowing more than 2mA to be sunk from the load. Now the sourcing chip drives the load in class A and the sinking chip provides active load. But there is a nonlinear crossover glitch at every point where load current crosses 2mA. This step in differential intput voltage appears on the output amplified by the noise gain of the circuit, which is typically about equal to the closed loop signal gain.
In reality, I made up the 2mA difference - it could be anything from zero to tens of mA as the guaranteed current limits are quite wide (see the datasheet). The difference of offset voltages and the magnitude of the crossover glitch may also be anything from zero to a few mV. Definitely not a reliable and reproducible trick and if you are actually hearing anything that isn't there otherwise, it is probably crossover distortion, although of a different sort than you will get from LM358.
I would test this with RMAA or something like that out of curiosity, but I wouldn't expect (positive) surprises. And the outcome may be highly random between samples and even between the left and right channel of the same stacked pair.
If driving opamps in class A is your thing, there are better ways.
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