I doubt they have a leg to stand on, but nevertheless, consult an attorney.

To be honest, it just sounds like they're trying to extort money; I doubt they'd follow through with an actual legal claim.

"Broken english, weird claim, demands money", that already fulfills 3 out of 4 criteria on the scam-o-matic scale. Did they say "hurry, or it will get more expensive" too?

Korean company, one of the poorest websites I've seen in my life... are you sure that the C&D letter comes from a lawyer at all? Seems rather unlikely that this is a serious claim.

But really, if you want to be safe, you have no option than lawyer up (and even then you're not safe...). Hopefully you got a legal cost insurance, since obviously Sang Ki Kwon isn't going to refund your expenses (between 10 and 190 Euros for a first counselling). Most likely you'll get "Well, it depends..." anyway, but not for free.

Personally I'd just ignore that guy, but that's me. He published his game a month before you published yours, so if it's reasonable to expect you worked on it for over a month (not doing it as a full-time job), it seems a tough challenge having copied any of it. For me, that would be raising a middle finger (especially since I'm not aware of any possibility for a guy in Korea to enforce such a claim in Bavaria).

If you have released this on the Apple app store then Apple have a system in place for protecting iOS developers. If the other developer wants you pull your game then they need to contact Apple and not send you a C&D. Your app is published by Apple and is sold in apples store if he wants your app removed he needs to tell Apple and then apple will send you an email either telling you to change something or that they are going to pull your app.

Apple have whole teams of lawyers in place who deal with things like this every day on behalf of its app developers who cannot always get a lawyer.

However, for now, I'll just reach out to that developer of "block puzzle" and ask him directly what's going on there...