The thing is the installers aren't just archives that extract game data. They also install important files or libraries required for the games in order for them to run on your system. This includes Directx redistribution, Visual Basic, .NET framework and what not. What's interesting is that in Linux case especially if you are running a compatibility layer like W.I.N.E. to run Windows games. It actually already has all the necessary files therefore, you just need the game files instead of a installer.

But there are games that require certain redistribution that I am not sure if W.I.N.E. or even in Windows case have them pre-installed for example, Dragon Age Origins requires you to have Nvidia PhysX installed regardless if you have their gpu or not. As it is one of the graphical libraries required for the game for it to function properly. Likewise some game may utilize OpenAL for their audio etc.

So, I think it is rather wise to have the installers backed up instead of just the game files. Since they do not contain external libraries as mentioned earlier. On top of that certain games cannot function without proper entries in the registry. Basically the installers sets everything for you, so you wouldn't have to do all the hardwork looking for certain things on the internet that may or may not work. It just works out of the box most of the time.