The Greek word used is Kosmos. Or Universe. There are several meanings however, many attempt to say Jesus meant Kosmino in which case why didn't he use that word? Unless he meant specifically as he said. The World. Or the entirety of humanity. Theoretically, then if every one in the whole world believed on Jesus do you believe they would be saved? I would say yes. However, Theoretically, by your account, if everyone believed on Jesus they could not all be saved but only the elect out of the whole. Because Jesus didn't die for those not elect.
Now comes the question of effective gift or not. If a gift is not in opperation it doesn't mean the gift is ineffective but the receiptient has not put it in opperation. And by doing so they have effectively rejected the gift. I think this is how scriptures reveal to us the nature of people who are condemned already.
The term "world" is used in many different senses in the New Testament. It is used for the "system" of evil that Satan is controlling. It is used for the physical system of God's created order. It is used as a hyperbole "turned the world upside down." It is used as a synonym for "gentiles" (Rom. 11:11-12).
However, in redemptive texts it is primarily used in a JEWISH context as in John 3:16 where the audiance is a Jewish theologion - Nicodemus. John wrote to Jewish believers (Gal. 3:9; I Jn. 2:2).
I think I can present a very good case that not merely the Jewish teachers but even the early Jewish church regarded the "world" in the context of redemption something unredeemable. For example, even after Jesus gave a WORLD wide commission the Jewish church did not obey it - they would not go outside of Judaism. Peter had to be given a vision three times before he would even enter the house of Corneilus and immediately upon entering he had these wonderful words to say:
And he said unto them, Ye know how that it is an unlawful thing for a man that is a Jew to keep company, or come unto one of another nation; but God hath shewed me that I should not call any man common or unclean.
It was so unprecedented that he took with him other Jews to witness it as he was going to be called in on the carpet by the Jewish church in Acts 11:1-17.
The first theologial issue was that gentiles had to become Jewish proselytes though circumcision to be saved (Acts 15:2).
The bias among Jewish Christians was so strong against including ALL RACES, GENDERS and SOCIAL stations as redeemable that John had to remind his Jewish readers that the propiation by Christ was not for them only but for "the whole world" - 1 John 2:2 - all classes and conditions of humanity.
Hence, my understanding of the term "world" in the context of redemption as used in the mouth of a Jew means "all classes, races and kinds of mankind" rather than "Jews only."
Hence, "For God so loved all classes, races and kinds of men" I believe is the correct understanding. The term world does not mean "all men without exception" but "all men without distinction."