So is this similar to the DCMA in the US, where there's a lot of iffyness about abuse and actually knowing that someone is actually a rights holder?
Not really, this is at a World level. Italy wants to ban an IP globally in 30 minutes.
DMCA take downs are domain specific with one provider. So scale is completely different here.
At least with DMCA you so get a notice and you can somewhat challenge it. With Italy's Piracy Shield you have no notice and there's no public record of which IPs/websited have been blocked, so it's hard to even challenge it in court.