So the "problematic" part this historian is saying is a "categorization" problem, where you have many different potential definitions of slavery, not all of which overlap, which creates problems when you attempt to overlay them with words that are being used to associate with slavery. This is already problematic amongst western languages, but even more so when you're trying to map chinese words and concepts into english.

My understanding of what he means by "problematic" is that he's trying to describe the level of "unfreedom" experienced by the eunuchs and the best he can come up with is "domestic slaves" but realizing at the same time that slavery has a specific set of connotations and expectations that don't exactly map with western conceptions of slavery.

There are parallels with discussions about slavery in the western classical world as well, namely "how does one define slavery?" For example, one latin word for "slave" is "servus," but depending upon the context as well as the time period, it could also mean servant, or serf. And as you can surmise, there's various "gray" areas of unfreedom each of those potential words carry that is very far from the classical image of the "fully oversought plantation slave" which acts as our standard bearer image for slavery.

So basically, though the historian was saying "domestic slave" is a problematic definition within the specific context of Chinese eunuchs, it is in fact a problematic definition throughout many time periods, western history included.

Hmmm. Any chance at a link? He might have been saying it's a tricky subject to discuss in China right now. Chinese eunuchs traditionally got a really rough ride in the historiography.