This neutral zone is a little unusual in that it doesn't actually provide you with much of anything useful. As soon as you arrive, an enemy combatant will actually attack you with his knife. If you shoot back at him, the security force will descend upon you for doing so. All that you can do is ignore him, or push him off the ledge by continuously hitting him with your grappling hook. You can also guide him beyond the zone guard and then shoot to finish him off.
Famicom version difference: for the knife soldier, it's possible to kill him with Iron Boots. This does not work in NES version.
Behind door A, you will find four bullets spread out throughout the room. Even expert players will find it incredibly difficult to collect all four before they disappear after six seconds.
Door B is even stranger. A grenadier waits in the room. When you approach him, he permits you to attack him and begins lobbing grenades at you. If you attack him, he will drop a bullet. And nothing more will occur. In general, there isn't much reason to visit here.