YES, exactly.

The 2nd Amendment establishes rights for the collective "people" while the other amendments establish rights for individual "persons." We know this because the authors demonstrate their knowledge of how to write "persons" when they mean individual rights and "people" when they wish to create a collective right. If the authors meant to create an individual right to own a firearm then they would have said so by stating "the right of all PERSONS to keep and bear arms shall not be infringed." They did not do so.

(Note: this is a basic test whether a judge is a activist hack or an impartial applier of the law.)

Congrats for your recognition that GRAMMAR HAS CONSEQUENCES!