It's not just a retelling of Genesis. The two things are completely different in theme, scope and focus.

The book of Genesis retells the story of the world's creation (there is a conflict in details there for these who notice), Garden of Eden, Cain and Abel, Noah's Ark, the spread of humanity, the story of the tower of Babel, the story of Abraham and Sarah and Isaac, The story of Sodom and Gonorrah, the beginning of Judaism, the story of Lot and his wife, Esau and Jacob, Jacob, Rachel, Leah. Jacob's wrestle with the angel, the story of Joseph who was sold as a slave and won the Pharoah's favor and died old in Egypt.

The most text is given to Abram, Jacob, Joseph, from a brief glance.

Now let's focus on Paradise Lost.

Satan features as a character in Paradise Lost, while he is not much mentioned in the Bible, mostly in the Book of Job (the word just means "adversary" in Hebrew and Arabic.) In Genesis there's no mention of him-- just of the Serpent who tempted Adam and Eve. The connection between the two was made later, theologically. It's not apparent in the text.

Milton creates a completely new narrative of Satan, makes him into a rebellious angel character, and gives him some of the best lines. ("Better to reign in hell than to serve in Heaven.") Milton shows him using rhetoric to gather his fellows, braving the Abyss alone, etc. sort of parallel but flip to Christ's days in the desert. There's an Angelic War. God wins and THEN creates the Earth and mankind. Milton in addition to making it clear that Satan is the serpent in the Garden of Eden, also weaves in the names of many demons found throughout the bible, making it clear they are the followers of Satan.

He connects the dots.

Meanwhile God creates Adam and Eve (in Milton's writing, Adam requests Eve as a companion, which diverges from Genesis) and gives them dominion over ALL creation (Genesis says "over the Earth" from the translation I recall), but on one condition that they not eat the tree of knowledge.

This part parallels/retells Genesis. But in Paradise Lost, we know more about Satan who is to be the Serpent, we know what his stake is in tempting them and getting them to eat the fruit-- if they lose control, then Satan and his angels can rule instead. But they all become snakes instead from God's punishment.

So it's a "villain origin story" as we would phrase it today, and an allegory of a political/religious war wrapped up in the legend of Genesis. Satan is presented as a complex character, almost as the hero of Paradise Lost.

God also is not presented as entirely good, since the fall of Man was part of his plan, himself being omniscient and omnipotent. The Son of God is not quite anti-trinitarian in approach but Milton believed the Son of God was secondary to the Father-- a doctrine of "subordinatism"

That he used blank verse to write an epic rather than a drama was a novel innovation. He knew his Bible and his theology and had the gift to put it in blank verse, and to create compelling characters with motivations and ambiguity. But because he interpreted the text in his theological framework and added in a lot more, it is not remotely close to a "retelling." One, he only retells a small part of Genesis, and he has set it up so it's a final battle, a climax, in the Angelic war.

Milton was writing at a time of great war, as Protestants and Catholics grappled, and that influenced his writing. He had lived through the English Civil War (Puritans vs the Cavaliers) and seen theater banned in Cromwell's England. Milton started formally writing "Paradise Lost" the same year Oliver Cromwell died, and also when his second wife and infant daughter also died. He had been blind for six years by then and needed others' help to write it all down.

The Continent was also in turmoil over religion.

So when he recreated the story of the Fall as part of a major religious war, nobody alive would have thought "this is just retelling Genesis." It's about the battle between good and evil, when neither side is quite as good or evil as one might think. Current events, recent history. Nobody really wins in a religious war. You cannot kill, deceive, betray, or manipulate others' dooms and follow the Commandments and thus stay holy.

What’s meant by “wildly and historically successful”? Does this refer to the success of Paradise Lost during Milton’s lifetime, or to subsequent success that lead to it being so well known today? Paradise Lost’s present day notoriety is largely due to a resurgence in popularity it enjoyed during the Romantic period when poets such as Blake, Shelley, and Byron “reclaimed” Milton’s Satan as a tragic antihero figure. This was especially true of Blake, who was practically fixated on Milton and said in The Marriage of Heaven and Hell that “The reason Milton wrote in fetters when he wrote of Angels & God, and at liberty when he wrote of Devils & Hell, is because he was a true Poet and of the Devil's party without knowing it.” Likewise, a lot has been written drawing a line from Milton’s Satan to the concept of the Byronic Hero. Paradise Lost is arguably so prominent in the western cultural consciousness more so because of its popularity during the romantic period than any popularity it enjoyed during Milton’s lifetime.

That said, it’s still important to root Paradise Lost in context of the time in which it was written and Milton’s life experiences. I highly recommend checking out “Milton’s social life” by Stephen B. Dobranski, an essay in the The Cambridge Companion to Milton. That whole collection is great for historically contextualizing not just Paradise Lost, but Milton himself. Dobranski says, “we need to approach [Milton] as a working writer and acknowledge the various social sites of his authorship. As epic poet and political pamphleteer; defender of divorce and supporter of regicide; teacher, businessman, and government employee.” All of these influences are apparent in close readings of Paradise Lost. I also feel the need to argue that Milton wasn’t just a Parliamentarian supporter, he was an instigator, writing not one but two works – Eikonoklastes and The Tenure of Kings and Magistrates – calling for the execution of Charles I in incendiary language.

Paradise Lost isn’t so much a retelling of Genesis as an expansion of it, a synthesis of Genesis, Revelations, and myriad classical texts. Reconciling classical texts with Christianity was a big thing throughout Milton’s poetical works. Milton strived with Paradise Lost’s structure to bring the heroic verse of Homer and Vergil to the English language. He wrote in his own preface to Paradise Lost that “this neglect then of rhyme so little is to be taken for a defect, though it may seem so perhaps to vulgar readers, that it rather is to be esteemed an example set, the first in English, of ancient liberty recovered to heroic poem from the troublesome and modern bondage of rhyming.” Milton was also very opinionated. (I pulled this quote from the Modern Library edition, which has modernized spelling.)

As for Paradise Lost’s popularity at the time of its publication, Anna Beer says in her Milton biography that it “did find a good many readers in the months and years after its publication in October 1667. The first print run of 1,300 copies sold fairly swiftly through the late autumn and winter of 1667, and was followed by three further impressions.” Milton had a reputation as an anti-monarchy firebrand by the time Paradise Lost was published, and this intrigued readers.

(Note: this is my first Reddit post ever. My wife showed me the question because I'm a huge Milton nerd, and I created an account just so I could answer.)

Adding to what's already been said, Renaissance authors wouldn't have seen Milton as "just" copying Genesis, or perceived "copying" as a fault in a work. The Renaissance concept of imitatio, or imitation, (which I'm drawing on G.W. Pigman's essay "Versions of Imitation in the Renaissance" in discussing), was influenced by the Senecan idea that poets were like bees who gathered from and digested various influences. Renaissance thinkers such as Erasmus, who were heavily indebted to this classical tradition, prized the idea that a poet might draw on and outdo their predecessors, with Pigman stating that this "attempt to surpass the model" was something writers at the time held to be different from slavishly mimicking a source text, and to be a creative act in its own right. This is reflected in the opening lines of Milton's poem, which recall the invocation of the Muse common to classical epic poetry ("Sing Heav'nly Muse"), but also states Milton's desire to outdo his predecessors and write about "Things unattempted yet in Prose or Rhime". In doing so, Milton was also making the case that an epic poem could be distinctively Christian in its themes--Homer and Virgil's epics were about pagan deities and heroes, but Milton is trying to show that this poetic genre can be squared with Christian ethics and beliefs.

I'll also briefly mention that the issues in the text were in some ways a very topical thing for Milton to write about (though my expertise here isn't as complete)--Milton was writing about a revolt against God in the aftermath of the English Civil War, where Milton supported the losing Parliamentarian side (which deposed the previous king). The precise nature of the poem's political commentary is much disputed (for instance, is Milton justifying a republican overthrow of monarchy, or is he presenting a difference between deposing a temporal king versus attacking God Himself?), but what's certain that Milton was drawing on issues of his time in reimagining the story of Genesis. For instance, in Book VI of the poem, Satan invents gunpowder cannons and uses them to do battle against the good angels; the presence of these "devilish Engines" is one of many things Milton adds to the source from Genesis to distinguish his text from its predecessors, in this case invoking contemporary memories of war as a parallel to the conflict in Heaven.