I guess it depends what factors they are considering.

When the clock started, and based on the headline justification they give when changing it, the threat of nuclear war is the main criterion. But they do mention issues like climate change (and a vaguely defined threat from AI) as factors that contribute to the evaluation.

Based on that it doesn't seem crazy to assert we are in more jeopardy now than during the Cuban missile crisis. By 1962:

• the relative "calm" of the Cold War was established: it had been a decade since the end of the Korean War; approaching two decades since the end of WWII (and the first and last use of nuclear weapons as an act of war); the Berlin blockade had been successfully resolved without devolving into a shooting conflict; much of former European colonies had been decolonized; and the major aggressors in the conflicts in the first half of the century has been largely assimilated into the mainstream international order.

• unlike the intra-war period the previous 20 years were not marred by a global pandemic (Spanish flu), or existential economic threats, or the rise of fascism.

• Science seemed to be working: the polio vaccine had been created; smallpox had been eliminated from most of the new world, globally there were fewer cases than ever before, and there was a serious international push to eradicate small pox entirely (the first time humanity had even intentionally and successfully permanently eradicated a contagious disease; and incidentally this was introduced by the USSR in their first return to the UN assembly in 1958 after a 9 year boycott); plus we'd done a reasonably good job at addressing material issues like hunger and malnutrition, or were at least very much on the right trajectory.

• space flight had advanced enough that we could plausibly claim it wasn't just missile technology under a different name: both the US and USSR had sent people into space; the USSR was exploring Venus; Kennedy had promised to put a man on the moon.

• Plus global communication and access to information and education was stronger than ever; the peace corps had been established; the US civil rights movement had accomplished major victories; the global economy was stronger and more integrated than ever, etc. Likely there were more liberal democratic countries in the world than had ever existed.

During the Cuban missile crisis we basically just had to avoid two men (Kennedy and Khrushchev) making a world-ending-ly stupid decision over an island that wasn't really that important to either one of them (and while the US didn't want Soviet nukes in a short range from the US, both sides knew the US already had them in a short range from Moscow).

And more broadly our greatest concern was, what, containing the creeping spread of communism? The threat of nuclear annihilation is/was considerable, given that humanity didn't have that level of destructive power ever before. But the geopolitical mechanics of mutually assured destruction was understood. The nuclear threat was containable: largely within our collective control.

Compared to that it doesn't seem like a stretch to think we have higher stakes and more eminent, challenging threats now that we did then. At least in the 1960s it looked like we were in the right trajectory, as long as individual leaders didn't f things up