I am, sadly, not a Tomcat driver, so I can't answer your questions. It may be they 1) Ignored the NATOPS, which is grossly unlikely, 2) Got a special dispensation from the CAG or boat's Capt., either for weight requirements for certain missions, or for a photo shoot. AB's do look really cool at dusk!
I know why the NATOPS specifies the "no AB" 2 engine launch. The engines are powerful enough, and spaced far enough apart that if they are in AB, and 1 has a bit of trouble, compressor stall, AB flame-out, fuel flow problem to 1 engine, whatever, and, during the cat shot 1 blower flames out for any reason, the yaw induced can be more than the pilot can overcome with rudder input before he can reduce the power on the other engine. A flat spin in the F-14 is unrecoverable in the first place. See the Emergency section of the NATOPS. Flat Spin-EJECT. Just one immediate action item to perform. No other things to try, no altitude or weight specifications, nothing. Flat Spin EJECT.
To have the start of one occur during launch, land or sea, is going to be fatal. Inevitably. If the yaw induced is fast enough, the pilot won't be able to reach the ejection handles, being pinned forward, and if the RIO doesn't act fast, and has BOTH selected for the ejection system, they will die, as well as loosing the plane. Let's face it, by comparison, planes are cheap compared to the cost of training pilots and RIO's. Forbidding AB launches obviates this situation.
I don't know the situations where the pictures were taken. It may be that at dusk, Mil Power creates flames similar to what the AB makes out the tailpipes, without actually being in AB. I just don't know enough about the engines to say, especially the D model Tomcats. I have read and reread the NATOPS when using the '14 in FSX, to try and make things as "real" as possible, but there are no explanations other than what you showed. I can find a number of places where the AB's are forbidden for launch, and I was always told by the pilots I could talk to when I was in that the NATOPS is law, so I presumed that it was. Like I say, special situations or permissions?
I know, not the best, but the best I can do...
Pat☺