It is not needed, but it is pretty much your only chance in court. The whole "mail yourself a copy" thing is a myth and pointless since as you said, just creating the thing is when you technically receive the copyright, not when you publish or register.
For videogames you can register the source code as well as tangible assets such as the artwork, soundtrack, and writing. I think it is similar to music where you can roll it all into one registration (for music, you can register the actual written music as well as a physical recording of it at the same time).
You don't get a copyright for some parts of it such as the name, or the gameplay mechanics. And yes, this process is probably not done by amateur developers who have some free projects up on itch. But I would think that anyone who is selling their game and netting even a small amount of revenue would be wise to get the registration.