It is remarkable that even the datasheet of the ESP8266 does not say anything detailed about the output impedance of this device.
It is important to match the output of the ESP to 50 ohm if you want to connect a coaxial cable to the device.
Also is it important to match the ESP-output to the antenna, PCB , ceramic chip or whatever antenna you use,
The reason for this is to transfer maximum power to the antenna so the device will give the best results and at the same time make the receiver's sensitivity optimal.
To me it looks like a lot of the ESP module's have no matching circuit at all and therefor will not produce optimal.
For instance look at the ESP02 where the output is connectod to an U-FL connector with only a small capacitor, I doubt this connector sees 50 ohms.
If you look at pictures of what is inside the metal can you find that sometimes there is this L-C-L matching circuit but often there is no matching circuit at all, only a small series capacitor.
I want to believe that some manufacturers of these modules have optimized there circuit by trial and error while using the right (expensive) equipment but some manufacturers will just do it as cheap as possible and will not use any matching at all just to save a few cents on these components and on design cost.