AndroidDynamicBinauralSynthesis-1.0.apk is the app itself. It can be downloaded and installed directly on the device. Note that you may have to tweak the system settings on the device in order to be able to install apps directly. See here.
AndroidDynamicBinauralSynthesis.zip contains the necessary data (audio scenes and HRIRs/HRTFs) to run the app. This file has to be unzipped to the root of the SD-card of the device. For more info on this see the infos in the project README.