I go by a de-facto interpretation. That way a country isn't defined by people wanting or not wanting to accept reality, but rather by facts on the ground.
Those aren't facts on the ground, they're legal fictions for another country.
Have you been to an un-recognised country before? I have. It's just... a country. Currencies, police, military, border security. Those are the facts on the ground. What their neighbours think are not.
Both are just as real interpretations. If a gang were to run a city it doesn't mean they start issuing passports that do anything or get to apply to vote on things in the UN. Just because you don't recognize the neighboring group doesn't mean they can't wage war against you or take control of what happens in the region.
For most contexts I'd agree being recognized by other countries is the most common interpretation between the two angles. That doesn't mean it's the only valid interpretation.
What happens when one country decides their claim extends into another's land? What if that land is populated by that country's culture? What about if they're of the other culture? Who, exactly, gets to determine who controls that land? Should we just have full on wars and kill thousands or millions of people for every single border conflict?
Or do we rely on legal fictions and group consensus to define rules on who gets to claim what?
Facts on the ground are I've claimed part of your country's territory as my own country. Your borders are a legal fiction.
Facts on the ground are you went on vacation, I broke into your house and now I live there. Your deed is a legal fiction.
If group consensus recognizes my claim over yours, my claim becomes valid and yours is not. I get the benefit of protection of the law. You, personally, can try to take it from me, but the police will recognize my claim and not yours.
If you claim part of my territory and group consensus rejects your claim, my armies and my allies' will enforce the legal fiction that is my borders and remove you from my territory.
Have you considered why these countries want legal recognition? If the law is fiction and facts on the ground matter more, why care about recognition?
The examples you provided are misconstruing the comment you are responding to. As they said, if an unrecognized nation has a systems for functional "currencies, police, military, border security", although I'd also add independent taxation, then it is functionally a nation. This is not a random declaration of sovereignty or declaration of conquest over an area they are referring to, but a place that has all of the elements of a nation or independent state, but is simply not widely recognized.
A well-known example of this is Kosovo, which operates as a sovereign state, with its own police, military, taxation and secure borders with border security, but is only recognized by only a little over half of the UN. Another example is Taiwan, which has its own currency, independent taxation system, passport, military, police and representative governance, despite not being officially recognized by many member states of the UN. Israel is an example of a nation which was not recognized by any of its neighbors, despite being in control of its territory, but ended up being recognized around the world all the same.
A country being diplomatically unrecognized, which is what was being referred to, does not mean that it is unknown or obscure. Both Kosovo and Taiwan are not obscure, but are still widely unrecognized.
The thread started on countries so desperate for a scrap of recognition that a single letter is extremely important.
When you point out countries that are only officially recognized by half the countries on the planet, that's not in the same ballpark. Those countries have widespread but not universal recognition.
For a proper example of an "unrecognized" country... I'd say for sure there should be less than 10 UN members that recognize it, and even that is an intentionally loose bound.