sensitivity vs impedance of headphone
There is no contradiction. You misinterpreted the article. Actually, impedance and sensitivity of a speaker are not  directly related to each other. Impedance says how much opposition it provides to the current flow through it, expressed in ohms. Sensitivity says how effectively an electrical signal is converted to sound. It is expressed in dBs/mW.  Both these factors together determine the loudness of a speaker, or as you wonder, how well it converts a voltage from amp into an audible sound.

If you have an amp of 8 ohms output impedance, then 8 ohm speaker is needed for maximum power output across it (Impedance matching). Now, the level of sound output depends on this power, and the sensitivity of the speaker. If you have another speaker with a higher impedance 16 ohms and same sensitivity, it will sound less loud for the same input voltage from the amp. Because, the output power of the speaker is lesser and hence the sound too. But here, if the 16 ohm speaker had a better sensitivity, it would have produced a louder sound.