The app doesn’t require or attempt to access any files on your phone/device, apart from its own files that are installed with the app (e.g. the many coin images).
Unfortunately Google does not use different nomenclature to differentiate your own media files and the files that are about to be installed with the app. Once the app related files are installed on your device, Google sees them as ‘your files’ and as the app obviously needs access to its own files (which are now classed as ‘your files’), the ‘Photos/Media/Files’ access permission is shown when installing the app.
The only other permission required when installing the app is the ‘In-app purchases’ which is to facilitate the upgrade to premium version (to show the values) for those that wish to upgrade.
The Check Your Change admin is Mr C H Perkins, publisher of numismatic publications in printed and eBook format. Author of "Collectors' Coins - Decimal Issues of the UK" and other books on British coins and related subjects.