cats that purr- aka those that have the bone in the larynx that allows purring (because tigers like our seme here can't purr, he can only roar and chuff) have different usages, frequencies and reasons for purring. when it comes to domestic cats in this case there are two noticeable types (solicitation and non-solicitation) to humans. variations can happen dependant on the cat and owner but purring as it functions can be anything. many kittens often purr and mother cats will communicate with purrs and trills so it just so happens that it serves a similar purpose w ppl.
aka to keep it short for my dumb ppl its specific to the cat itself so assuming its them being content is not 100% true, they could be trying to get something out of you or trying to self soothe.
funny fact i found is that cats often purr when theyre in pain but in specifically during birth/labor when the cervix relaxes, or during contractions as someone mentioned above that is working as a coping mechanism. i'd also like to mention that sex when it comes to cats is NOT enjoyable so theres probably a non zero chance a cat could purr after something like that. i think maybe the author intended it to sound like he liked it but honestly lowk it could go any way you interpret that

he has no idea cats dont purr because they like something FAKE CAT OWNER!! /j