Just because you cannot see any sign of God(s), it does not mean that God(s) to not exist. The more extreme for of atheist says that because they see no evidence of God, and they can fully explain the Universe without God, therefore God God cannot exist. They argue that since a Creator would have to be more complex than His creation, you must assume the simplest case - that the Universe pooped into existence on its own, rather than that God popped into existence and then created the Universe. I find this excessive. I am happy to agree that there is no sign of God operating today, and that the Universe could have come into existence with out a God to create it. But the fact that it could have does not mean that it did. Give me a statistically valid sample of universes and the information as to whether they were created by Gods, and I will have an opinion on the matter. As it is, I will have to say firmly that I do not know what created the Universe, and God is a perfectly tenable hypothesis. What the nature of that God might be, I cannot surmise, so there are no rules about worshipping etc. I therefore live as if there were no God, until information to the conrary reaches me.

There's no affect on atheist reasoning. Atheists don't believe because there is no proof of god. Your quote is the opposite.

It doesn't necessarily affect atheistic reasoning at all. It is true that an absence of evidence is not necessarily evidence of absence - but within reason. For example, there is no evidence that planet-sized, invisible unicorns orbit the moon on Sundays. This lack of evidence does not mean they are not there - but based on everything we do know about our surroundings we can say the probability of them existing is extremely low or zero. With gods the logic is similar. Every god or goddess so far has failed to produce evidence of their existence. Based on what has been learned about the universe, our planet and ourselves we can say the probability of a god or gods actually existing is pretty low...

Other answers have explained your quote. So I'll explain why your quote doesn't affect atheism at all. If you want to talk about evidence, consider a courtroom. (I live in the US, so I'm going to talk about an American courtroom) The court starts from the presumption that a defendent is not guilty. It is up to the prosecution to prove that he is guilty to the satisfaction of the court, by presenting evidence of his guilt that the defense is unable to disprove. If the prosecution succeeds, the court will conclude that the defendant is guilty and will act accordingly. If the prosecution fails to prove its case, the court will conclude that the defendant is not guilty. I am the court. I start with the presumption that what I don't see in front of my eyes doesn't exist. Someone can change this presumption by showing me evidence. Like, I'm a kid in school and my teacher shows me the world is round by showing satellite photographs with the curvature of the earth, and I conclude that the teacher must be right, and commit this new knowledge to my memory. If they are unable to prove their evidence to my satisfaction, or contrary evidence disproves what they've shown me, I will discard the theory. Again, I'm a kid and the evidence of presents being under the tree and cookies and milk having been consumed from the plate no longer convinces me that Santa Claus came down the chimney after I catch dad hiding the christmas presents in the attic. In the case of evidence for a god, it's the same - there's no evidence to convince me that one exists. If new evidence comes up, sure, you get a retrial. But I'm not going to hold off a verdict indefinitely just because you need more time to work on your case.