The Flood was a universal judgement.
"And, behold, I, even I, do bring a flood of waters upon the earth, to destroy all flesh, wherein is the breath of life, from under heaven; and every thing that is in the earth shall die."- Genesis 6:1
"...if He did not spare the ancient world when He brought the flood on its ungodly people, but preserved Noah, a preacher of righteousness, among the eight;"- 2 Peter 2:5
Now what does "universal" mean?
including or covering all or a whole collectively or distributively without limit or exception
Well, according to Merriam-Webster.
So this means that the Flood was a divine judgement that God inflicted on anybody living in the ever-so ancient days of Noah. No discrimination was present in who He was going to judge- destroy all flesh.
Their ages, socioeconomic status, gender, nationality, religion, personal circumstances...all of that did not matter when the Flood came. It was a broad and sweeping judgement, literally.
Now the question is, can the word "universal" be used in cases where you're really just talking about all the people around you and not literally, everybody in the world?
Yes, for example, it is not wrong for a nation to say that they have universal healthcare, even though they are really just referring to the type of socialised healthcare that is solely applicable to that nation. Another example includes the notion of universal suffrage. It's not wrong to say that all the adult citizens of, for example, USA have the universal right to vote when really, we are referring to a right that exists only to a certain group of people in a particular area of the world.
Likewise, on a daily basis, we wouldn't come and call someone who expresses "I'm going to destroy the world" to be in error if they only destroyed the world that they individually know of.
The bottom line here is that for something to be called universal, it must be collective, distributive, without exception/limitation and most succintly, broad.
This accurately describes the nature of God's judgement in using the Flood, whether one interprets it to be local or global. Everything must die, except for Noah and his family. There's no time for "What about them?", "Who sinned?", "Who did what?". The only words that one could justifiably say back then was, "Time's up! Board on or be boarded."
So when God says that he will never send a flood like the one in Noah's days, all He means is that He'll never inflict it in a way that disregards the factors and circumstances of all the sinners involved (and targeted) in this fearsome judgement. But that doesn't mean God will one day judge the world, this time, on a much more catacylsmic and horrific scale. On that day, it will be fire.
"But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up."- 2 Peter 3:10