What you're talking about is a legal issue, so if you want to keep the game in its current form (or do some changes to avoid being sued) you need to speak with a lawyer. Said lawyer (or person who understands IP law) would need to look at the two products side-by-side and tell you what the exact issues are. Also keep in mind that the even if other party is wrong they can still throw lawyers at you in the hopes that you'll go away.
I think this is an over-reaction. It didn't look to me like a threat per se. Of course, I don't know the entire context.