Nuclear Non-Proliferation Treaty
And North Korea isn't breaking any issues surrounding international law because they are not party to the Nuclear Non-Proliferation Treaty.
That's simply not true. Click the status link of your own source and you will find that the Democratic People's Republic of Korea joined 12 December, 1985 in Moscow.
You might be arguing that North Korea has since left the NPT, but there's no provision to leave. The agreement was that if North Korea (and others) joined, they would be given access to peaceful uses for nuclear reactions (see here). In particular, they could access information not available to non-members. North Korea accessed such information. They cannot now enjoy the benefits of that and ignore their responsibilities.
It is misleading at best and downright dishonest at worst to describe North Korea as not a party to the treaty. It certainly signed. It received benefits (which is how it developed its nuclear reactor that it uses to enrich uranium for use in nuclear weapons).
Despite maintaining a no - first - strike policy (unlike some other nuclear possessing states).
There is exactly one country that has ever used nuclear weapons to attack. That country (the United States) of course used them in a war where its territorial sovereignty had been violated. So there are zero uses of nuclear weapons that have ever been used in a way that violates the policy that you are calling "no-first-strike" (the North Korean policy). So to say "unlike some other nuclear possessing states" is misleading at best.
Several people have pointed out that this is not really a no-first-strike policy. That's fine. Then North Korea does not have a no-first-strike policy, whatever they may call it. Which makes this particular point singularly worthless. This is what they are calling a "no-first-strike" policy.
Indeed every other country which possesses nuclear weapons use exactly the same argument (deterrence) to maintain their right to possesses nuclear weapons, so why is only North Korea criticized?
Other than North Korea, only eight countries have nuclear weapons. Four of them were the victors over Germany in World War II: US; United Kingdom; France; Russia (as the Soviet Union). The other four are China, India, Pakistan, and Israel (undeclared). Perhaps the world would be better off if that list were shorter. But it certainly won't be better off making that list longer.
Israel is a small country created after an attempted genocide that is surrounded by countries that deny its right to exist. Four countries started developing nuclear weapons in response to Germany (with some extra Cold War drama for three of them, so they finished after Germany was no longer an issue). China developed them because it considers itself one of the big three militaries and both the US and Russia already had them. India developed them because China had them and Pakistan wanted them. Pakistan developed them because India was.
Pakistan is the only other country that achieved nuclear weapons after the end of the Cold War. It did so in response to India and rather shortly after the end of the Cold War. And its example shows part of why North Korea is being criticized today. Pakistan shared nuclear secrets and missile technology with North Korea, Iran, and Syria.
North Korea doesn't need a nuclear deterrent. It already has a Seoul deterrent. Its artillery are capable of killing the majority of the citizens in the capital of South Korea. From whom but an ally of South Korea do they need defense? Russia? China? Their big worries are South Korea and the US, but South Korea is deterred directly. The US is far more likely to attack a nuclear North Korea than one with conventional weapons -- it changes North Korea into a danger to US citizens.
North Korea engages in regular cyberwar attacks to steal money and knowledge from other countries. Their version of a "no-first-strike" policy would allow them to answer even proportionate retaliation with a nuke. Not to mention the possibility that they might argue that South Korea is part of their sovereign territory. Or they could simply drop the policy altogether if it got in their way, as they dropped compliance with the NPT.
In the past, North Korea has used the threat of attack to extort money from other countries. There is a widespread belief that if they had usable nuclear weapons, they would use them in extortion.
In general, many people think that North Korea is more likely to use nuclear weapons than those countries that have them. Many also think that North Korea is more likely to exchange nuclear knowledge, equipment, and/or materials for money or oil. There are allegations of them trading chemical weapons to Syria. Second source.