Disclaimer: This is speculation, because I haven't read the actual law (and I'm not Italian, so it's not like I really have a reason to).

I would assume that they will handle it like this:

To be able to sell your VPN service in Italy, you'll have to get accredited. Since you're now taking Italian customers' money, your company's dealings in Italy fall under Italian law. They might be able to extradite you, depending on what country you operate from, but realistically most businesses don't want to get involved in that kind of stuff, because even if you don't get extradited, no one wants to be put in a situation where they need to actively avoid a country.

This leaves free VPN services, right? Well, since ISP and "legal" VPNs need to conform to the new law, the Italian government could blacklist those VPNs' websites (which all ISPs and legal VPNs are required by law to block within 30 minutes of them being added to the block list). So now, you're in an awkward position as an Italian if you want to get a VPN that doesn't follow those laws.

I'm not sure at what extent this law goes, or how they handle people who are paying to circumvent it (because you might have bought a VPN before this), but they might simply require that banks refuse to process payments from VPN providers that refuse to get accredited.

Obviously, they can't really block this thing without going the Great Firewall route (and even that has ways of being bypassed), but that's not really their goal here. Their goal is to establish a stranglehold on what the everyday citizen does. It's to put a framework in place that allows them to quickly and efficiently block content they deem you shouldn't be able to see. It's a disgusting display of a government overreaching and censoring what their citizens' have access to on the web.