This means that a game is supplied in the 32-bit flavor only. This should not cause any problems on a 32-bit system, however, 64-bit Ubuntu and Mint distributions only come with 64-bit libraries pre-installed. A 32-bit application requires a matching set of 32-bit libraries, therefore it might be necessary to install additional packages from repositories.
A list of required libraries for each game will always be available in the requirements section of the gamecard.
If you want to install most required libraries ahead of time, you can do so by performing the following commands in the terminal (enter your user password to unlock root priviledges):
sudo dpkg --add-architecture i386
sudo apt-get update
sudo apt-get -y install libc6:i386 libasound2:i386 libasound2-data:i386 libasound2-plugins:i386