Klaymen and other important characters were not actually animated via traditional claymation. They were mostly made out of painted latex figurines housing a brass armature. This lent them the needed stability and also kept them from deforming too much and possibly falling apart or melting, which would have happened to traditional clay models.
According to the creators, the game carries Biblical messages and was primarily based on the story of the fall of Man. The Biblical allegories are most evident in the Hall of Records, an enormous and literal wall of text about the Neverhood's backstory, which reads like an affectionate Bible parody and features characters representing God, Jesus and other figures of Christianity. Creator Doug TenNapel himself is a devout Christian.
Despite positive critical reviews, the game only sold around 42,000 copies because point-and-click adventure puzzle games were not popular by the time of its release. However the game built up a devoted fan following and became a cult sensation, and fans helped fund the development of a similar game, _Armikrog (2015)(VG)_ by the same creators. It was also especially popular in Russia and Iran thanks to large-scale bootlegging.
At least two references to Christianity can be found in the game; the story in the Hall of Records is in fact a parody of the biblical story of man's fall from grace. As for the other, listen to the song that can be heard in "Sound Effects Record #33" during the radio puzzle, it is in fact the song "Kumbaya" played in reverse.
The trivia item below may give away important plot points.
In the good ending of the English version, Klogg cries "Son of a... !" as he gets hit by the cannon and flung out of the Neverhood. In one of the game's Russian translations, he actually finishes his curse.