Sigh, I don't want to be here, yet here I'm again, thanks rei and anon x3.
Just mass DMCA the site if it gets out of hand, if the host is in the US affiliated country, it will be gone. The key is that legal action must be followed through if the site owner doesn't take it down.
Translated work is derivative work, only the translator(s) own the rights to their version of the translation. That isn't to say the original author can't DMCA the translator(s) if the work is publicly accessible (one of the criteria to determine violation and monetary damage). The author only owns the commercial rights, they does not have ownership of the translation by default. So translators can still keep their version of the translation for private use as long as it's outside of public access (including fee-based access).
tl;dr author rights > translator rights in commercial use. translator rights > author rights outside of commercial use.
Hosting vs Directory
Directories, like aho-updates and novelupdates, are fine as they are not diverting traffic or access away from the businesses (not qualifying one of criteria for violation of copyright). I believe there was a case precedence involving Yellow Pages that clarified the law in question (for US and subsequently Canada) and it was subsequent expanded to allow certain techs to utilize excerpts in search engines (thumbnails were at the risk of violation otherwise).
Hosting it without permission outside of Fair Use is pretty much automatic violation.
Fair Use for dummy
Is the translation dissected/commented extensively (substantial additional work beyond the translator(s))?
Is it used as a part of an education program, course or scholar research where substantial work done by the researcher is visible?
Has the work been substantially altered for use as satire/parody?
Is it in discussion as a matter of public interest, as represent in journalistic outlet and otherwise with additional works (critique, commentary, etc...)?
If yes, you are fine for Fair Use (differences in different countries). Best to consult a lawyer/solicitor if legal issues do arise though.
The site in question fail in every aspect, no amount of screaming fair use will save it since it's violating multiple key components that are required for fair use.