I was reading some PDF titled “Roman Polygyny” PDF here reading mostly from the sections “What were slave women for?” (pg 18-20) and “But whose children were they?” (pg 20-26)
There was alot about how folks would go out of their way to make sure male slaves would remain chaste. They were barred from marriage, and in around pg 20 Juvenal said slaves were beaten if they even attempted to mingle with a woman.
And apparently most people born into slavery were born between a master and a slave woman, while very few slave men became fathers. Unless I’m misinterpreting this, which I hope I am, a lot of female slaves were basically breeding stock by their masters meant to produce other slaves.
Meanwhile if a male slave were to be found in a relationship with a free woman, that woman could become a slave as punishment.
I think a later law was made that allowed a free woman to pay the master to mingle with a slave, but her children legally became the master's slaves. I also read that from a PDF Free Women and Male Slaves, or Mandingo meets the Roman Empire
Male chastity really wasn't a thing people cared about IIRC, not like every man was out and about getting laid but the ones that did didn’t seem to get flack for it unless they were part of an oppressed group. I have ideas on why but they kinda border the whole "Alpha vs. Beta male" drivel. So why was that? And is there a better name for it?
So, I gave that article a quick once-through. I have to say I'm not impressed with the writing or research. She's clearly using translations, not her own, and sometimes from secondary sources, which is just lazy research. This article is also published in a book she edited, so it's not peer reviewed. Neither of those things are indictments of the ideas she's proposing per se, but they are red flags. There are some other things that popped up, like citing Xenophon on the economics of breeding Roman slaves. That makes no sense. Xenophon was a 4th C BCE Greek author. He had never been to Rome, and probably knew very little about Rome. I don't know why you would look to him for information about Roman economics.
Betzig herself is an anthropologist by training, not a historian. She also seems to be published in non-historical journals. I'm looking through her CV. I see one article published with a co-author in Classical Journal; everything else is in psychology or sociology or popular venues.
As far as the article itself, I didn't see a lot on male slave chastity. There's a sentence on barbarians being unlikely to have a female partner, and something about owners wanting to maximize the sexual availability of their female slaves (basically rape whenever they wanted). Very little about male slave sexuality, except they were also available to be raped. There's one reference to Cato charging his male slaves for access to his female slaves. I don't think this article has very much to say to us about your question.
It is worth remembering Roman family relations were legal relations. The father had to be Roman for a child to be a Roman citizen, until Hadrian, and then both parents had to be Roman citizens. The Latin Right allowed legal marriage between Romans and Latins, and if Latins moved to Rome they could gain the citizenship. Manumitted slaves gained the citizenship. Soldiers in the Empire who served enough years (varies by period) could gain the citizenship. Apparently the centurion that was going to whip St. Paul bought his citizenship somehow (that story is a huge mess). Inheritance had to pass between Roman citizens though. If you are dying and you want your kid to get your stuff, they have to be recognized as legal Roman citizens.
In the earlier period, keeping male slaves from breeding, as Betzig notes, would leave female slaves more available to masters, who might be able to reproduce, sure, and on manumission might have a citizen heir, but that's not really an argument against male slaves having sex lives generally.
I am inclined to suggest that Romans were more interested in slaves as sex objects (look at Roman comedy) rather than sexual entities with their own desires, and hence they appear as objects to be used rather than people to be indulged. I don't know any reason to suggest that male slaves were kept celibate.