Apple has moved fully to Apple Silicon (M1, M2, M3 chips) and 64-bit architecture. Office 2013-era software is 32-bit. If you are running macOS Catalina (10.15) or later, the DMG will open, but the application will simply refuse to launch. You will have wasted time and risked your security for nothing.
Microsoft ended all security updates and technical support for Office 2013 on April 11, 2023 . Using it today, even on Windows, poses significant security risks. Modern Alternatives for Mac Users
Microsoft Office 2013 for Mac: Alternatives & Compatibility Tips
– Sometimes Microsoft 365 is included with your email provider or school account.
: The "ribbon" interface and updated visual style seen in Office 2013 for PC finally arrived on Mac with the release of Microsoft Office 2016 for Mac .