Windows: run the installer. If SmartScreen appears, click More info → Run anyway (the app is unsigned). The game keeps itself updated automatically after that.

macOS: open the DMG and drag Happy Pets into Applications. The first time, right-click the app → Open (it's unsigned). Updates are automatic afterwards.

Linux: x86_64 AppImage. Make it executable (chmod +x HappyPets-*.AppImage) and run it. Updates are automatic afterwards.