For some unknown reasons the developers of wireguard-apple project did not release .dmg files and the only way of getting the app is to download it from App Store. Yet that requires sign-in into an Apple account.
After the application is downloaded one can sign out the Apple account and just use and transfer it to other MacOS devices by simply moving the app into Applications directory. This repository contains universal (Intel & Apple Silicon compatible) application to save you the hassle.
To install it simply download a release, extract the application, and put it into global or local Applications directory.