What is the proper way to uninstall game

What is the proper way to uninstall game installed by make install?

checkinstall is so much better than “make install”. It will create package for your distro (e.g. deb for Ubuntu) and install it. And uninstall or upgrade can be done using package manager.

On your question - there is no such command but you can manually remove all files.
List of files installed by vcmi, should be complete:

/usr/lib/x86_64-linux-gnu/vcmi <- 32-bit systems
/usr/lib/i386-linux-gnu/vcmi  <- 64-bit systems
/usr/share/vcmi/
/usr/bin/vcmi*   <- 3 executables
/usr/share/applications/vcmiclient.desktop

Note that prefix can be “/usr/local/” instead of “/usr/”