I guess he mean the square wave looks like distorted sound, which is dangerous for the speaker.
Distorted sound are sending DC signals through the speaker, which will heaten the coil and in the end burn it.
But I doubt its dangerous in this case, there usually are some capacitors somewhere in the nes or amplifier circuit that will prevent clean DC signals.

What is more dangerous is to play your amplifier too loud, which makes the signal to clip and DC will be outputted.
Actually, most cases of failing speakers depends on a too small amplifier, not too big.