Well the law is surely addressing European/Italian citizens and business. If you serve them from the US and target Italians for financial gain, you are no longer extraterritorial because you operate there as a business.
Italy has authority over what Italian companies or subsidiaries are allowed to do, and they have authority over any operations that foreign companies have within Italy and any dealings that foreign companies have with Italians or others in Italy. They do not have authority over foreign companies operating in foreign countries serving foreign customers, just because that company also does business in Italy. That is extraterritorial, and is what this law is requiring by demanding that Cloudflare remove DNS entries worldwide.