In fact the argument is correctly stated the opposite way.

If you have an amplifier with a 2 ohm output impedance, the maximum power can be delivered into a 2 ohm load.

However, in an audio environment we need to consider the rated output of the amplifier. If it is rated as delivering 100W RMS into 8 ohms, we should not expect that it has an 8 ohm output impedance. In face, as Bob has suggested, the output impedance will be substantially lower.

The lower output impedance improves the "damping factor", and this is essentially a benefit of the impedance mismatch. Indeed an amplifier with an output impedance equal to the load impedance would have quite poor performance.