Perhaps they shouldn't be games, but a new object type 'Modifications', which have a single relationship to a game/engine, or if you could tag a game as a Modification and it automatically gets a new field added which allows this relationship to be added? But differentiating is hard. Is Garry's Mod a mod or a game?
I like The Beasts idea it would be an easy way for people to find mods specifically for their games, this way people wouldn't have to know the name of a mod before hand. And with Garry's Mod, a mods a mod until it is sold.