Ah, that's good that you knew about phasing. From memory, I think speakers are usually marked so the cone moves outwards towards the listener when you apply the voltage with the marked polarity, but you can't rely on that, especially if you're mixing manufacturers; you need to test each speaker with a AA cell or similar. Also I wouldn't rely on the pop being of the same polarity for both channels. It probably is, but I wouldn't rely on that.
Yes, the way the chip is designed means that its output pins do pretty much the same thing regardless of loading (unless they're overloaded by a speaker with too low resistance). It's a Class D amplifier, which means its outputs are constantly switching between GND and VCC at a high frequency. What is, or isn't, connected to the outputs doesn't make much difference.
The exception is mentioned in the data sheet: if external LC (inductor-capacitor) filtering is used, it's possible that the output stage could be damaged because of the voltage-generating characteristics of inductors. But that circuit doesn't use external LC filters, and removing the speaker reduces the inductance, so there's no problem.
Amplifiers that do require a load aren't designed deliberately to have that characteristic. It's a by-product of other design decisions that were made for other reasons, and the designer decided the benefits outweighed the disadvantage.