The phrase "such compulsion" refers to a strong urge or force that drives someone to do something. It means being pushed or pressured to take a particular action because of a compelling reason or motivation. Full definition
The paintings would be silly if they weren't so intense and felt, and painted with such compulsion. (theguardian.com)
Awareness of this point, and of the extreme suffering that accompanies such compulsions, should make us sympathetic toward Christian weight - watching. (religion-online.org)
Food lovers refuse to accept such compulsions over longer period of time. (pear-shaped-gal.com)