Yeah, until any details are provided, I would just assume that the ISP already requires that users install some kind of software, and they just pushed the malware through that program.
From what I understand of the autotranslation, the ISP planted the malware somehow and that malware interfered with the P2P system, but no mention of actually using the P2P protocol to spread the malware
You don't need to install any software to use the internet at home in Korea. You just get a modem that connects to fiber at one end and exposes an ethernet port (or wifi) at the other end. Just connect to that port and you're online immediately.
ISPs also provide TV and a bunch of other services, though, and some of them might require installing specific software in order to use on a PC. Or perhaps they hijacked an unencrypted download of someone else's software, most likely some component of the file sharing service in dispute.
I reckon they used a good old fashioned honeypot. Seed a torrent of some random popular content that also contains malware payload, and let users download it.