They merely affirmed the right by putting it in their constitution - they already had shall issue licenses previously for the common man, both for ownership and carrying for defense.
This is more interesting:
Maybe you ask why this additional constitution law helps us to secure our civil gun ownership against EU restrictions, because EU restrictions are more powerful than basic laws of EU countries – this constitutional right is just first step. The second step, which will follow and already is in our parliament and senate for discussion is, that the our government – especially our Ministry of Interior affairs in, collaboration with Ministry of Defense, make a project which is called “defined state backups” and that means that all gun owners can sign to a special training with guns covered by state armed forces. This course should deepen the civil gun owners skills to defend lives before special police forces arrives. It is our reaction on terrorism and the cases with active shooter in schools, public areas, etc. We know that the police cannot be everywhere. That means that all the gun owners which undertake this training and make a promise, will become let’s say part of interior security. The interior security is one of a fields where EU has no rights and then we can say – OK, you cannot tell us which kind of guns or size of magazines we can have, because this is strictly in our competition for our internal safety.
Basically, with recent EU laws, they restricted things like military style semi-auto rifles, pistol magazines over 20 rounds, rifle magazines over 10 rounds etc. Exceptions were made for what is essentially the militia. So by doing this, they can ensure that everyone can still have comparatively easy access to modern rifles and full capacity magazines.