This was another story I felt was trying to be Lovecraftian, but just not managing to pull it off. (In fact, I am pretty sure this was a Mythos story - some of the muttering of the crew referenced some Mythos motifs, right?) The notes are there, but there is no music.
Firstly, the story lacks Lovecraft's pulpy thrust and directness of plot. I feel like it meanders in the beginning. Losing its way. There is little plot to be seen and only a vague attempt to build the ice up into a nemesis. I felt the story particularly failed at this: the ice, the environment never felt threatening. Compare this to a story like "The Left Hand of Darkness" by Ursela Le Guin and see what I mean.
Secondly, the Lovecraft elements felt tacked on. Creatures emerge from the ice shelf, yes, but their dicovery is made neither dreadful nor monumentous. I felt the idea of a primordial thing frozen in ice is so overused it has basically become self-parody at this point (Giant Octopus vs. Mega Shark, for example). There was nothing of the awe or majesty embodied in the discovery of the nightmare Plane of Leng in "At the Mountains of Madness."
Thirdly, the narrator suddenly seems to know that these creatures and the "big daddy" one will destroy the world. That seemed an unlikely jump. In "call of Cthulhu" the world-shattering power of the deity is slowly built up, but in this one it's just sort of tossed in.
Fourthly, and I would admonish all Lovecraft-imitating authors to remember this, Lovecraft never let the horror be the horror. He always made the horror the final piece in a puzzle that implied much, much worse. Here we have a monster. In "Call of Cthlulhu" when the big guy appears, we know that here is not just a monster, but the slumbering doom of mankind.
Fifthly, another thing I would remind all Lovecraft imitators to remember is that the horror should never be the final horror. There should always, always be implications of far worse. In "At the Mountains of Madness" the unfortunate scientists discover the horrible, black mountain range covered in the ruins of an aeon-dead civilization and still host to the last of their monstrous progeny. Yet even these horrors are TERRIFIED of the purple mountain range, even larger, even more distant. Always let the secret of the abyss be that, at its heart, it conceals an even deeper, blacker abyss.
In summation, I felt the author invoked a lot of Lovecraftian concepts - but that's it. She did not do the heavy lifting required to transform them from "Boo! A monster!" to the cosmos-shaking doom of stars.