That's a pretty good overview.
Tactical nuclear weapons were definitely available and were expected by both sides to be used either in the first assault or within three or four days of the first strike. Chemical and biological weapons would be used immediately.
Certainly if the battlefield nuclear weapons were not used in a first strike to blast open a hole in the NATO defences or vaporise the advancing Soviet forces, then they would be used later as the war began to drag out.
IIRC the Soviet plan up until the early 1980s did call for a massive use of nuclear weapons on the first strike, but also assumed that NATO would do the same on Soviet deployments and bases.
Obviously, once that starts, then it's a case of progressing to ammunition dumps and airfields, which are usually near towns and cities. The UK would receive some golden sunshine on its airfields, and would likely retaliate in kind with ICBMs and Vulcans, which would then trigger the Soviets to retaliate in a mass strike on cities (since they wouldn't know where the missiles were going) and then the US would launch back, which would prompt the Soviets to launch the rest and....well...
I do like that the lesson plan simulates the disjointed nature of NATO, probably one of its biggest weaknesses, that a consensus needs to be reached on plans before they can be enacted whereas in the PACT they are dictated to the other members by the Soviets.