The Green Goblin has always been an unusual nemesis for Spider-Man. His secret identity famously led to bad blood between his creators (true or not), and even his theme makes little sense in context. Why, out of all of Spider-Man's animalistic enemies, is the worst of them a goblin? Why was the color of that goblin important when he was the first goblin-themed villain on the scene? Different writers have offered different answers to these questions, usually leaning on the strong connection between Peter Parker and Norman Osborn. But Osborn isn't the only villain to have taken on the Green Goblin persona, and when Loki donned the mask, the unusual villain became stranger and more dangerous than ever.
While the Green Goblin has generally been a threat to Spider-Man when an Osborn was under the mask, the persona has also been used by heroes. Philip Benjamin Urich was briefly a heroic Green Goblin, the denizens of Marvel's Earth X have a complicated relationship with the mask, and Peter Parker even briefly adopted the persona when Norman tampered with his mind. So it's not unprecedented that the Goblin be someone other than an Osborn... but it is unprecedented that they'd be a god.
As befits an Asgardian god, Loki's time as the Green Goblin didn't involve the usual bank robbery and corporate espionage. Instead, the God of Mischief targeted just one person during his reign of terror: Norman Osborn. At the time, Norman Osborn had replaced Nick Fury as the head of America's strategic defense force, dismantling SHIELD in favor of his own HAMMER organization. More than that, Norman's "Dark Reign" came with enhanced legal powers, allowing him to force many heroes underground and elevate super-villains to their former positions. Norman also founded the Cabal - a gathering of Marvel's most influential villains - which is when he caught the eye of Loki.
Irritated by Asgard's then-residency on Earth and preparing a labyrinthine plot involving his own rebirth, Loki saw the famously unstable Osborn as an opportunity to turn earthly power to his own ends. Indeed, throughout Osborn's tenure as HAMMER director, he was haunted by the maniacal ramblings of his alternate persona - first speaking through his former costume, then as a monstrous goblin figure. Few readers questioned Osborn's breakdown - his criminal insanity was well established by Marvel history - but the true nature of his "haunting" was revealed in Dark Avengers #12, when the goblin figure looming over him was replaced by Loki. Siege: Loki by Kieron Gillen and Jamie McKelvie expanded on Loki's plan, which was part of a long con necessitating a war between Asgard and Osborn's HAMMER forces.
Loki may not have tugged on an armored costume and climbed aboard a goblin glider, but he deliberately took on the guise of the Green Goblin in order to further his villainous ends, making him as qualified to claim the dastardly title as most of the other characters who have worn the mask. Setting him apart from the likes of Harry Osborn and Phil Urich is just how successful Loki was as the Green Goblin, instigating a huge battle that killed scores of gods (including Ares, the Greek god of war, and many Asgardians whose souls were destroyed thanks to Loki) and got him exactly what he wanted. Even at his most unhinged, Norman Osborn's entire career as the Green Goblin doesn't have anywhere near the body count of Loki dabbling in costumed villainy for just a few months.