You're wrong, I know for a fact that you can (and should) register your product (including the name) in Europe. I guess what you're saying only applies to US but the author is European, hence my advice.
When you register you specify your work, the name and the sector it belongs to (films, novel, web sites, etc.) and you get a document that testifies your rights over it. I know this because I used my filing to have Google remove a clone of my app from the store. It was a lengthy process, but with the registration you can have leverage.
"In general, registration can serve as prima facie evidence in a court of law with reference to disputes relating to copyright."
I'm pretty sure you can get a more formal copyright paper if you file it. However, it doesn't matter and you could even do it after the fact if someone infringes your copyright.
Registering your copyright entitles you to damages in court. It's quite valuable.
Edit: to be clear, with an unregistered copyright, you can still sue for an injunction to stop someone from distributing your material. You won't get your statutory damages, though.
The code and look / feel does fall under copyright though, so if it was using the same graphics or it can be proven to be using the same code (or a decompiled version of it), it can be removed under copyright law.
But yeah. This is kinda why people patent stuff, despite the brouhaha about patents: if you don't patent your gameplay idea (in this and similar cases), people will just take your idea, rebrand it and run off with it.