When Littlefinger sent a whore to Prince Joffrey's bed, he proceeded to kill her instead of having sex with her.
Also, the TV show had shown or hinted lots of sex scenes, but Joffrey wasn't in even single one of them.
It was also not that he was in love with his fiancé or other girl.
Being a teenager, why wasn't he interested in sex?
As you've pointed out, the implication is that Joffrey is sexually active but there was a significant out-of-universe reason (according to the actor who played Joffrey) for not having any explicit sex scenes involving his character, namely that his character was portrayed as being only 14 years old.
“Even though that would have been technically legal, I think the character Joffrey was probably about 14 or 15. I don’t think that would have been appropriate. But I think there is some male nudity in the show. As I say, I don’t watch it so I can’t really comment, but I have heard that there is male nudity—so I think that is one good thing, to not just objectify women but also objectify the beauty of the male genitalia! We’re all objects together.”
Obviously the makers decided to have Tommen and Maergery in a scene together in a subsequent season, but this very chaste by comparison to some of the other steamy scenes seen in the show.
I didn't read the books or watch the series, but even I know that in the books Prince, and later King, Joffrey was a preteen for most of his life. I think he was only 13 or 14 when he died, and if so he wasn't very far into his teenage years when he died. Thus the Joffrey in the novels might not have reached puberty and might not have been much affected by hormones before he died.
In Game of Thrones the television series the creators hired an actor who might have been close to a decade older than Joffrey, deciding to do so for various reasons which I have not researched.
So if the creators of Game of Thrones tried not to make too many changes in the plot during the early seasons, and if most of the changes were omitting characters and plot lines for reasons of time, they would not have added too many plot details in the early seasons.
So maybe they never got around to writing scenes, that were not in the books, where Joffrey showed much interest in sex, despite the fact that the actor portraying Joffrey in Game of Thrones looked old enough to have a many times stronger sexual drive than the child Joffrey in the novels.
Asexuality is the lack of sexual attraction to others, or low or absent interest in or desire for sexual activity.1[2][3] It may be considered a sexual orientation or the lack thereof.[4][5][6] It may also be categorized more widely to include a broad spectrum of asexual sub-identities.[7]
Further empirical data about an asexual demographic appeared in 1994, when a research team in the United Kingdom carried out a comprehensive survey of 18,876 British residents, spurred by the need for sexual information in the wake of the AIDS pandemic. The survey included a question on sexual attraction, to which 1.05% of the respondents replied that they had "never felt sexually attracted to anyone at all".[34]
King Joffrey behaves like a psychopath, a personality type which I hope is very rare. I see no reason why the older King Joffrey in Game of Thrones might not also have another rare personality type, being asexual.
Or it is possible that the older Joffrey in Game of Thrones might have a different personality type in which his sexual desires and urges are satisfied by acts of violence.
This is just speculation.
