It is not property owned or leased by the federal government. The clerks are not postal employees. It is not a post office. If selling selling stamps was the only requirement for being a post office, then lots of other stores would qualify, too. Your own home might even qualify, since you can now print postage at home thru stamps.com. IANAL
It's also not even clear that the post office has the power to prohibit the carry of firearms in its facilities when doing so is not against local law. I have often wondered how it can be simultaneously illegal to carry a firearm in a post office and yet not illegal to mail one. If possession of firearms is illegal in a post office, what's the difference if it's in a box with an address on it or in your holster? Handguns are nonmailable except by "dealers" (which, interestingly, the definition doesn't include C&Rs, who are FFLs and can lawfully engage in interstate commerce of C&R handguns, but still not mail them), but rifles and shotguns are mailable by just about anyone, including nonlicensees. A dealer's FFL doesn't grant one the authority to carry a handgun in a post office either, but it does grant the ability, if the proper paperwork is included, to mail one. It seems as if the USPS wants to have it both ways, both accepting the business of mailing firearms while not allowing the carry of firearms. But that in itself creates a problem, as both the holstered carrying and the mailing of firearms both require possession on federal (leased or owned) property.
There's also at least a plausible argument that the actual regulation that the post office cites is broader than the statute that allows it, and thus it's invalid as a legislative regulation cannot be broader than its parent statute. I wouldn't recommend violating it to find out what a judge would say, and as many of you have pointed out for yourselves, I am not a lawyer either. And it's been a few years since I actually read the regulation, so I'm not familiar with its substantive content.
Neither of these points have any bearing on a gas station as post office, as people have pointed out, because a gas station isn't a post office.
FYI, Kroger and most banks sell stamps too....no worries mate