He's only 39, right? I was a teenager for OWoD and I'm ten years older.
I mean, my brother got VtM 1E in 1991, he was 11, I was 13. Revised came out in 1998 and the oWoD was still going pretty strong in 2000, when Coogler would have been, what 14/15? Coogler has a middle, maybe even upper-middle class background - he went to private school, for example (and not the low-rent "just for the religion" kind, the kind with a strong academic reputation and boarders and so on).
So it's highly possible, even somewhat likely he had some exposure to RPGs as a teenager, and VtM would still have been one of the "big boys" at that time (when I was at Uni in 97/98 it was by far the most popular RPG being played, the only one with multiple tables, and it had three).
On the other hand he's never mentioned it, and it's also possible it entirely passed him by - a lot of stuff which had strong VtM-ish vibes in the 2000s turned out to be by people who had definitely never played it, but were Anne Rice fans and fans of stuff like Near Dark, Lost Boys, etc. - I mean, you combine those two factors and you basically can recreate all of VtM except the "clans" from first principles.
My personal feeling is that is that he probably didn't, but other people on the film probably would have, and it's easy to imagine that might have had some influence on how the Chicago 1993 scene was presented.