Germany has regulated it, (though states have slightly different regulations, some states even allowing online gambling, some banning all except the government run lottery).
Technically no, because EU directives aren't applied as written. They're goals for member states to make into national laws, which intentionally leaves them some leeway.
However, national law must reasonably satisfy EU directives, otherwise CJEU could determine that a member state is infringing EU law and fine them until they amend their law.
So it should be possible to regulate it.