Looking at the context in the verses, we can see it was not some little neighborhood local supposed 'whole world'.
Ge 1:26 -And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.
Ge 6:12 - And God looked upon the earth, and, behold, it was corrupt; for
all flesh had corrupted his way upon the earth.
Ge 6:13 - And God said unto Noah, The
end of all flesh is come before me; for the earth is filled with violence through them; and, behold, I will destroy them with the earth.
Ge 6:17 -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.
Ge 7:19 - And the waters prevailed exceedingly upon the earth; and all the high hills,
that were under the whole heaven, were covered.
Ge 9:11 - And I will establish my covenant with you; neither shall
all flesh be cut off any more by the waters of a flood; neither shall there any more be a flood to destroy the earth.
Ge 9:17 - And God said unto Noah, This is the token of the covenant, which I have
established between me and all flesh that is upon the earth.
The bible makes it clear only the people on that ark lived.
1Pe 3:20 - Which sometime were disobedient, when once the longsuffering of God waited in the days of Noah, while the ark was a preparing, wherein
few, that is, eight souls were saved by water.
The old world does not refer to a small area.
5 And
spared not the old world, but saved Noah the eighth person, a preacher of righteousness,
bringing in the flood upon the world of the ungodly;
"
And spared not the old world…
In distinction from the present world, that now is; which was, as it were, formed anew out of that which was destroyed by the deluge. The Vulgate Latin version renders it, "the original world"; and the Ethiopic version, "the first world"; it designs the ancient inhabitants of the world, as it was from the beginning, before the flood; who, being wicked, were not spared by God, but had just punishment inflicted on them:"
2 Peter - Chapter 2 - Verse 5 - The New John Gill Exposition of the Entire Bible on StudyLight.org
I mean do you really claim that this verse refers to some small area??
Heb 11:7 -By faith Noah, being warned of God of things not seen as yet, moved with fear, prepared an ark to the saving of his house;
by the which he condemned the world, and became heir of the righteousness which is by faith.
"Another theological problem arises when we come to
Genesis 9:11–15. God made a promise to Noah and his descendants that “never again shall there be a flood to destroy the earth.” In other words, God was promising never to send another event like the one Noah experienced, where we are told specifically in
Genesis 7:21 that “all flesh died.”
Obviously,
if the Flood of Noah were only local in extent, then because we have seen lots of local floods since the time of Noah, that have destroyed both man and animals, God has broken His promise many times over! To the contrary, this rainbow covenant God made with Noah and his descendants could only have been kept by God if the Flood were global in extent, because never since in human history has a global flood been experienced."
Was the Flood of Noah Global or Local in Extent?