I was wondering what's up with both of these movies coming out in 1999 and I then I remembered what that decade leading up to it was all about: The X-Files. On the face of it, since neither movie has anything to do with aliens or government you would think 'eh, nah' - but the theme is conspiracy. Shadow group, hidden power, and in the Ninth Gate case, 'bringing something about', too. There's a thread from that 'end of the millennium' 'something's going to happen but we have no idea what' tension, through the X-files, to Ninth Gate.
Of course these two movies are from books and probably long considered by their creators, but there's a question of which project gets picked, both by polanski/kubrick out of their ideas, and by the people financing, 'green lighting' etc. The 90s had a 'conspiracy' mood, entirely due to X-Files, and so I think without it these movies would not have happened, or not in 1999.
See also the 2000 game deus ex (aka 'the conspiracy') for another example and maybe 'the holy blood and the holy grail' as another influence, certainly on that game, it's where the French angle with the old Chateau concept comes into it. But you also see that kind of location in these movies