This is totally absurd.
I agree with many of the replies here saying that this big guy is trying to bully you out of your domain name and most probably acquiring your domain for their use (because of the s in your domain? Give me a break man...)
Imho, you can settle it through a combination of the helpful solutions offered by our fellow forum-ers here.
1) Consult a lawyer, showing him the "get ready for consequences letter" and see which lawyer actually do this kind of verbal threat (might come from a phony guy for all we know)
2) Check out the ICANN website provided and actually it should rule in your favor as you started this website before they acquire a similar name domain later on, the WHOIS details should be able to prove it (Prepare this one early)
After everything is done, maybe get your legal representative to send the counter party a letter with all the necessary details so they might cease and desist or should they wish to carry on, at least you know you are not actually committing the offence of copyright infringement.
Just my 2 cents worth and all the best to you!