So someone mentioned that lawyer is probably better placed to offer advice to you on this issue. While that's true and you can't really be wrong by saying that, I think there's a degree of personal common sense applicable here albeit with the caveat that as a random forum user I could be completely wrong and it's not my ass on the line.

I've seen similar things to this before when companies join torrent swarms and then contact the ISP to which swarm member's IP addresses are associated and ask them to send emails to the owners of those IP addresses with similar threatening sounding stuff. You never know if you'll be really unlucky but on balance, these guys are probably fishing (not phishing although really, kinda phishing). They haven't asked for anything in particular from you except that you stop what you're doing. To respond would basically confirm that you are the owner of the server and likely imply that you specifically, knowingly distributed copyrighted materials. They haven't compelled you in any way to respond so it's best not give them that gift.

They did say don't delete anything and my lack of legal knowledge prevents me from saying confidently to what extent they really can do that, but I strongly suspect that if push came to shove you couldn't really get in to trouble for deleting things given you could well never have received the email or had some kind of a problem with the system causing you to lose data, however you can bet that your plausible deniability would be greatly constrained if you respond, therefore acknowledging that you have seen their request that you not delete things.

TL:DR you don't have to reply and you definitely shouldn't, and also, they asked you to stop, so stop.