The sniffing relies on people trading files using p2p connections (and exposing their IPs) and lawyers getting the user of the IP at that time from internet providers, either via court order or some other back channel. There is no deep packet inspection.

Some lawyers are even using sites similar to https://iknowwhatyoudownload.com/

It probably costs less to pay the amount than fighting it in court. I think it's capped at 450 Euro or something? But I know some people who got scot free by merely having a lawyer send a response.