We are on the brink because NK will not stop their nuclear programme and missile tests.
The USA have said they will take unilateral action against them in the event of another test.
Should the USA do this NK are threatening the use of nuclear weapons (hopefully sabre rattling and their nukes are very limited and short range but could hit SK or possibly Japan).
The USA might respond in kind to a nuclear launch from NK. However I think they are more likely to respond with conventional weapons.
Russia and China are both allies of North Korea.
If the USA launch a preemptive strike against NK then it is not clear where China would stand (though I do not think they would side with NK - they are more concerned about a destabilised NK and the refugees and volatility this would create in the area along with not wanting a unified Korea, but still - they will not look favourably on the USA making a preemptive strike).
Russia have already warned the USA about not taking unilateral action against NK. This could easily lead to a war between the USA and Russia. Russia have moved anti-aircraft missiles close to the NK border and both China and Russia are following the US Navy deployment in the area. If Russia and the USA go to war, China may well side with Russia.
Trump and Putin are highly unpredictable and both have committed to increasing their nuclear capabilities. Trump asked 3 times in a security meeting just after taking office what was the point of nuclear weapons if they couldn't use them and has been obsessed with them since the 1980s. All current Russian war games end in a nuclear deescalation scenario (drop one and ask for peace). Trump did not get congressional approval for the Syria airstrikes and did a complete U turn on previous policies, showing he is capricious and does not feel the need to seek the approval of his own congress, let alone the UN / NATO.
The Doomsday clock has moved forward 30 seconds due to the Trump / Russia / China / NK issues and that was before this week when things started really kicking off.
So yes, I'd say we were on the brink given all of that.