Technically, the code is alleged to violate copyright, not DMCA. A DMCA notice is just the process that copyright owners use to tell service providers about allegedly infringing content.

The argument is for contributory copyright infringement via inducement, ala MGM v Grokster 545 U.S. 913 (2005) or Columbia Pictures Industries, Inc. v. Fung 710 F.3d 1020 (9th Cir. 2013), the isoHunt case. Inducement occurs where someone distributes a device with the intent of promoting infringement and actual infringement occurs. Here, the argument is that nyaa intends to promote copyright infringement because it provides a tool that is tailored for copyright infringement. The notice letter cites various references in the code to nyaa.si. Exhibit A of the letter comprises "a series of screenshots taken from the Nyaa.si website for the Project that include images of copyrighted works available through the Project." The implication here is that the devs here are encouraging similar use of the code for infringing copyright.

I'm not saying I agree with it, but that's their argument.