Del Toro is one of the three most surreal of the three genius of Mexican filmmakers that burst into the consciousness at roughly the same time. The other two are Alfonso Cuaron and Alejandro Innaratu. The 2010 Academy Awards were dominated by the visions of all three and there's a bit of visual grandeur in all three. None will forget the imagination shown in Gravity and Birdman, variations on the same cinematic trick done completely different ways.
Del Toro's visions have a certain level of humanity in all of them, but its often covered by bleakness. Who can forget the captain at the center of Pan's Labyrinth, the most frightening monster in a surreal world? Or Michael Shannon's character tracking the Creature from the Black Lagoon in The Shape of Water. Nightmare Alley has just debuted on HBO and I expect to see it shortly. Maybe its not a horror film in the traditional sense, but based on what you described in your review, it is a monster movie even if the monsters aren't in the league of Hellboy. Del Toro knows who the real monsters are, and that they're the scariest.