I don’t see giant as being “elemental” in the Aristotlian alchemical sense that D&D elementals are.
I am referring to them narratively as elemental chaos associated there in the 4e elemental origin lore that giants had in 4e. The elemental chaos has a bunch more association with Chaos in my mind than the pre-4e elemental planes. Mixing disparate elemental themes in 4e elemental chaos monsters to create hybrid elemental combos was common in the first three 4e MMs.

5e combined the pure elemental planes with 4e's elemental chaos and had the chaotic hybrid areas be close to the prime and at the borders of the four elemental rings as they make a circle.
4e MM:
GIANTS ARE HULKING HUMANOID CREATURES with fundamental ties to the world, be that bedrock, uncontrollable fires, raging storms, or inevitable death. The first giants were massive titans of fire and frost, storm and stone. These giants labored under primordial lords to shape the newly forming world.
In the eons since the first days, giants have multiplied and moved on, finding places to call their own in planes beyond the Elemental Chaos, including the Shadowfell and the Feywild, and even in the realm of their masters’ deific foes, the Astral Sea. However, giants prefer the world their labor helped create, and giants of every variety can be found upon it. Indeed, when the primordials retreated from the world, one of the first empires of that dawn era was one created by giants, and their slaves were the children of Moradin. But those heady days are long vanished.
4e Monster Vault:
Shortly after the world emerged from the smoldering forges of the primordials, titans stepped forth to help explore and shape the new creation. They walked atop the world’s still-cooling crust and swam through its churning seas, yet even in their immensity, the titans were too few to explore the vast world. They created giants as a servant race, modeling them to resemble the titans’ own elemental natures. With the aid of the giants, the titans spread out across the world. In time, the giants enslaved some of the nascent races of the gods, most notably the dwarves. Under the giants’ steady gazes and heavy hands, these industrious slaves brought beauty and refinement to the world.
A Shattered Legacy: When the Dawn War began, titans and giants joined the side of their creators in the battle against the gods.
4e DMG:
The Elemental Chaos and the Abyss
At the foundation of the world, the Elemental Chaos churns like an ever-changing tempest of clashing elements—fire and lightning, earth and water, whirlwinds and living thunder. Just as the gods originated in the Astral Sea, the first inhabitants of the Elemental Chaos were the primordials, creatures of raw elemental power. They shaped the world from the raw material of the Elemental Chaos, and if they had their way, the world would be torn back down and returned to raw materials. The gods have given the world permanence utterly alien to the primordials’ nature.
The Elemental Chaos approximates a level plane on which travelers can move, but the landscape is broken up by rivers of lightning, seas of fire, floating earthbergs, ice mountains, and other formations of raw elemental forces. However, it is possible to make one’s way slowly down into lower layers of the Elemental Chaos. At its bottom, it turns into a swirling maelstrom that grows darker and deadlier as it descends.
At the bottom of that maelstrom is the Abyss, the home of demons. Tharizdun, the Chained God, planted a shard of pure evil in the heart of the Elemental Chaos before the world was finished, and the gods imprisoned him for this act of blasphemy. (This story is told in more detail in the “Demon” entry of the Monster Manual.) The Abyss is as entropic as the Elemental Chaos where it was planted, but it is actively malevolent, where the rest of the Elemental Chaos is simply untamed.