Skybird, the video appears to be only in German so I could not look at it in its entirity, but the US was not the only one to blame for rising tensions in the early 80s.
The Soviet Union invaded Afghanistan in 1979, forced Poland to impose martial law and crush the "Solidarity" movement in 1981, shot down flight KAL 007 in sept. 1983 killing 269 civilians.
The rise in military spending in the USA was more of a reaction to Soviet moves than the other way around. Since Reagan's diary has come out, we now know that he was personally opposed to nuclear weapons.
On another note, I am not convinced the early 80s were worse than the 50s and 60s in terms of coming close to the brink.
In the 1962 Cuban crisis, the USSR sent 4 diesel submarines to Cuba, each armed with nuclear torpedoes. The Captain of each could order their use on his own and each was given only the vaguest of ROE, basically "use you best judgement". At least two of the subs were intercepted on the high seas as part of the blockade and were forced to surface after lengthy hunts by US ASW TFs. Thankfully, none of the Soviet skippers was a hot head...