From the question:
I could only think of "compellement" but I fear it is not a word, or the state of being compelled exists in a different form than what I can guess.
As was stated in a comment under the question, the noun is not compellment, but compulsion:
1 a : an act of compelling
// tried to get them to cooperate without using compulsion
: the state of being compelled
// He was acting under compulsion.
1 b : a force that compels
2 : an irresistible persistent impulse to perform an act (such as excessive hand washing)
// her compulsion to repeatedly check and recheck the stove to be certain that it is turned off
also : the act itself
// Gambling is a compulsion with him.
So, the example sentence becomes:
As opposed to doing it out of addiction, he did it out of [a] compulsion for the art".