Weirdly enough that is not unlike the gun law here in Ireland except that it's the local Police who decide. Nothing was actually banned just certain weapons considered as 'very dangerous' and subject to special consideration. So in theory you could buy a fifty calibre machine gun and get a licence if you could convince the local Superintendant. Only in theory. In practice even a .22 LR was tough to get.
But that was challenged in court recently. The shooters won and now in theory you can buy handguns and larger calibre rifles if you can justify your use of it. Handgun owners who lost their guns in 1972 when they were taken into 'tempory custody' are demanding them back. There are even ads for handguns in shooting magazines all of a sudden.
The same thing would happen in the US. It would be thrashed out in the courts once and for all if they tried to enforce a law with that kind of wording. The courts would be clogged with appeals.
One other point on the so called EU attempt to ban personal gun ownership. That would cost an enormous number of jobs. Names like Steyr, Benelli, Beretta, Glock, CZ etc etc would disappear. Basically it's ridiculous.