The equality of all mankind is not a Jewish idea. It is a Greek/Roman/Western-democratic idea that Jews have assimilated over time. Humanity does not all exist on one level. Let's look at how Rabbi Moshe Chaim Luzzatto, ztz"l explains it with commentary provided by Torah.org's Rabbi Yaakov Feldman...
PART 1, PART 2, PART 3
Derech Hashem, Part II, Chapter 4 - Israel and the Nations, Paragraph 6
 The decree, however, was not that the other nations should be destroyed. It only meant that they would have to remain on the lower level that we have discussed. This lower state would never have been meant for man if Adam had not sinned. It only came into being in the first place as a result of his sin.
These nations still have the human aspect, blemished though it may be, and God desired that they should at least have a counterpart of what was actually appropriate for all mankind. He therefore granted them a Divine Soul (neshamah) somewhat like that of the Jew, even though it is on a much lower level. They were likewise given commandments, through which they could attain both material and spiritual advantages appropriate to their nature. These are the seven [universal] commandments given to the children of Noach.
All this had been arranged from the beginning of creation, prepared for the contingency that man would sin. In this respect, it is like other harmful things and punishments, which were also created conditionally, as our Sages teach us.
Torah.org - Rabbi Yaakov Feldman
As we pointed out (2:4:3), the dynamic behind the chosenness of the Jewish Nation comes to this. G-d favored Abraham because he elevated himself; and we Jews, his offshoots, have thus been chosen to carry out Abraham's G-d-centered mission. We learn as well that each and every other nation plays a unique role in the great scheme of things, but not that one.
The other nations aren't to be scorned, and their efforts to draw close to G-d Almighty aren't to be denied. For each and every human has been created in G-d's image (see Genesis 1:26), and thus has an immortal soul as well as a consequent yearning to return to its Source.
We're also taught that non-Jews have been granted mitzvot and thus direct Divine guidance as well.
Those mitzvot are referred to as "The Seven Noachite Laws" (named after Noah, the second father of all of mankind after Adam, who was granted them himself). Thus non-Jews are bidden to avoid idolatry, blasphemy, murder, sexual impropriety, robbery, eating the flesh of a living animal; and they're to set up judicial systems as well. It has been pointed out that each one of these seven mitzvot implies several subcategories, and that there are thus actually some sixty to seventy mitzvot involved, all told.
Still and all, though, the existential reality is such that non-Jews remain on the level of man in his fallen state, unlike the Jewish Nation.
Derech Hashem, Part II, Chapter 4 - Israel and the Nations, Paragraph 7
 In the World-to-Come, however, there will be no nation other than Israel.
The souls of righteous gentiles will be allowed to exist in the Future World, but only as an addition and attachment to Israel. They will therefore be secondary to the Jew, just as a garment is secondary to the one who wears it. All that they attain of the ultimate good will have to be attained in this manner, since by virtue of their nature they can receive no more.
Torah.org - Rabbi Yaakov Feldman
As everyone knows, you can tell the content of a person's dreams -- as well as the quality of his being -- by the rewards he hopes to earn for his efforts. And as is also true, the less appropriate his reward, the less pleased a person will be, and the less effort he'll make. That goes for a person's material as well as his spiritual dreams.
So if you value the life of the spirit and pursue metaphysical goals your whole life long, you'd be terribly disappointed being rewarded by a grand banquet, say, in the end, no matter how opulent. And you'd be disappointed to be rewarded by a set of esoteric religious texts, for example, no matter how profound, if you had striven for wealth your whole life long.
Now, as we'd depicted it, the reward due a person in the World to Come is closeness to G-d and the experience of basking in His supernal light forever. Obviously, some people would consider that an off-putting prospect and would do all they could to avoid it.
Ramchal's point here is that since nothing swells the heart of a true descendant of Abraham more than closeness to G-d in the World to Come, which was Abraham's ultimate goal, then we'll indeed be rewarded with it.
His other point is that those non-Jews who strove to draw close to G-d by adhering to the seven Noachite Laws will also earn a place there -- but a lesser one. Because they'd have done less to draw close to G-d here (i.e., they'd have fulfilled less mitzvot) than we had.