I can posses one but not purchase one?
That's how I would understand the law that you posted. You would not be able to go to a local gun store and purchase a handgun, but you would be able to shoot one at the range. The range may have their own separate rules. Furthermore the way I read it, it looks like the law was written allowing someone over 18 to own a handgun (for example through inheritance, or buying through a private seller who is not an FFL). Straw purchase would be illegal.
IANAL and TINLA