It most definitely days the right of all people.
The single complete thought of the sentence is "the right shall not be infringed". That's it. Subject. Verb. Predicate adjective. Take that away and you do not have a complete sentence in english grammar.
Everything else provides additional information.
What right? To keep and bear arms
Whose right? "Of the people"
Why? A well regulated militia being necessary to the security of the free state
Maybe the framers were trying to be eloquent, for all I know, but if they wanted arms restricted to a militia, there are a million ways to make that abundantly more clear than what we have.
You literally could say "the right of the militia to keep and bear arms shall not be infringed". Then it would unquestionably apply the 2A specifically to the militia.
I know the grammar of the 2A has been debated at length. You'll find parties arguing both interpretations (militia vs. people) and the infamous comma argument, which I find comma-cal (had to pun) because it's entirely irrelevant. Comma or no, the subject and verb are the same.
A proper diagramming of the sentence tells all. Thanks mom (grammar teacher of nearly 30 years).
All that to say, yes further regulation is necessary because "shall not be infringed" is not synonymous with "cannot be regulated".
Edit: normally I don't post this early/late but I woke up and my brain is firing on all cylinders