It would appear that this was the Titan IIIE which launched Voyager 2. They would have had another chance to get the shot about two weeks later when Voyager 1 launched. (Due to quirks of interplanetary orbital mechanics, Voyager 1 got to Jupiter several months before Voyager 2 despite launching second).

The IIIE did indeed have a Centaur stage with a "thermos" full of liquid hydrogen and another with liquid oxygen, but that's not what we see in this clip -- the pillars of fire and smoke come from a pair of solid-fuel boosters that burn for about two minutes, followed by about six more minutes of flight powered by two more stages burning non-cryogenic liquid propellants (hydrazine and nitrogen tetroxide) before the Centaur was ignited.

For those wondering, it's actually quite common that two spacecraft launched that way (if two spacecraft are launched, which is not common) would arrive out of order. The reason is that you can think of a "launch window" as really a specific ideal launch time, but a little earlier or later will also work, although being early or later would result in arriving at the destination later. They aim to launch the first spacecraft right at the opening of the window, so if there is any delay they won't run out of time. If it launches "on time", then it actually launched early for the launch window, and takes longer to get there. The second launch right after then launches closer to the actual ideal launch date.

Decades ago, I worked a mission that went up on a Titan IV, and I spent a few weeks at Pad 41 working in the IUS clean room. Riding up and down the tower in the rickety (self operated) elevator was frightening. Walking the gantry and looking out at CCAS, you could see for miles in all directions. Standing under the thrust cones was an amazing experience. Unfortunately, no photos were allowed because it was a classified mission. All I got were a few stupid tee shirts.

About 15 years earlier, I had done some work at the VAB and walked around the Saturn IV that was laying on its side there, just as James Burke had a few years earlier. It wasn't there when I worked the above referenced mission. I'm not sure when they moved it, or where it ended up (but it's not in the "rocket garden" at the Visitor Center).