Basically, the cable only changes the assignment of the contacts - otherwise it does nothing. Have you checked whether this microphone is really being used by the video app or whether it is the one on the mobile phone? The best way to test this is to tap lightly on the microphone. If you don't hear any plop noises on the recording, the built-in microphone of the mobile phone is recording. The data sheet says: "... and using the RODE Rec app for iOS". I use the RODE Lavalier Microphone on Windows PC and Android phones with a similar adapter and it works.
If it has a jack for a headphone (headphones with microphone, TRRS is more or less standard for smartphones - except for the new Apple models), then yes! See: https://www.nodch.de/how-to-externe-mikrofone-mit-dem-android-smartphone-nutzen/3444/