The reason it doesn't make sense to you is because you are assuming it is applied in an ideal perfect universe, while the statement is referring to the real world, where any retributive rule is applied by imperfect actors who make errors in the assignment of culpability (both in identification of who is responsible and in identify whether their act was justified in the first place.)

Such errors result in people who shouldn't be blinded themselves being blinded, and are themselves the subject of retaliation by the same error-prone process.

>An eye for an eye would leave two people blind

Well under your reading wouldn't it just leave them each without one eye. They may be blind but in most cases they will still have one other functioning eye. /pedantry

"Who paid retribution for the second blinding? The second paid for the first, I demand a third eye" ... ergo the aphorism.

That's correct, the only problem is it takes thousands of years for humanity as a whole to agree that the consequence is too severe to stand. On this time scale, the idea of not fighting wars because they cause damage is relatively new.