The problem isn't necessarily IMDb, but the fact that it's a little too short and lacking guidance.
First of all, you might be confused about the timeline a little here.
Here is the new definition, as it appears in our official documentation...Removing the the reference to IMDB was entirely the right move.
That isn't actually "our new definition". This has always been our definition to some degree. It's a phrase coined as early as the first meta discussions on the matter. It's not like we had the IMDb version first and then decided to scratch that for the help center, they're complementary.
But I also don't get the reasoing in this sentence:
Removing the the reference to IMDB was entirely the right move. We don't want basic "cast and crew" questions that IMDB is great at answering.
If we don't want these questions, then why does saying that we're not that site that actually has the answers to these questions a bad thing. I'm not saying it's necessarily a good idea to mention IMDb, but that reasoning for not mentioning it doesn't quite make sense to me. Either the sentence is missing a word or I'm not entirely getting what you're after there.
Now to the actual reasoning for why it's there. This close reason is primarily supposed to shield us against two (slightly related) things.
First of all, the part that is indeed answered by IMDb or any other referential site, the useless credits queries for "who played this guy?", "what's that song called?", "when did this guy direct his first feature film?". We're not bothering with stuff that is perfectly answered with a link to the credits of the film. And for that the IMDb reference was quite useful, since in the film field that seems to be somewhat of a referntial database for all your factual needs and we aren't trying to duplicate that in any way.
The other category that's related but much more fuzzy and a cause of contention often enough are questions that look like useless trivia but which can often be turned into proper questions by just giving that extra bit of motivation for why the question ought to matter to anyone beyond just useless bar talk curiosity, as elaborated in this answer. However, this category is quite a bit more subjective to determine and, as said, is often a question of wording and is actually more what the "does not add to the understanding or appreciation of the title" phrase alludes to. Song identification questions are good example for that. It's not like we close them all as "trivia", only when they fail to make a connection to the film.
The proposed wording as taken from the help center is quite fuzzy, which has the advantage of covering quite a few things, but also the disadvantage of not always bringing across the point and being quite a bit subjective, as seen in this related discussion. I don't see the wording you propose on its own helping on the front of making this category less fuzzy and cutting down on people jumping on the close-vote button over the edit button a little too quickly. I do like it, though, and it's somewhat ingrained in this site's manifesto to a large degree. So I would still build upon it, but maybe extend it a little.
Now okay, you don't want IMDb in there, we don't have to have it in there. But I'd still like to catch the useless reference questions that ask for who that guy is or what that cool song is called.
But I'd also try to encourage people to motivate their questions beyond just trivia and actively work on improving them. Since often enough people have a reason why a question adds to their appreciation of a title, they just need to tell us and share that appreciation with us so we understand. But then we come along and say their question is useless. Well, it might be, but making it useful often isn't beyond a few additions to the question text.
Maybe the problem is that we're mixing two different close-reasons into one, but I don't think the "trivia" reason can't catch both of the above things. We don't really have to bother much with the first one as to improving, since usually those things are beyond improvement. But the second one on the other hand is often salvagable and I'd encourage more improvement over just scratching it off in that department.
With the above points in mind and in congruence with the structure of our existing close-reasons, I'd propose, as a first start for discussion, something like this:
Trivia questions that do not add to the understanding or appreciation of a movie/TV-show are off-topic; We're not trying to duplicate IMDB. Please try to explain why your question is relevant for understanding the work beyond banal minutiae.
Yes, yes, the dreaded IMDb reference is still in there, but I really struggle to come up with an equally short but to the point way of saying exactly that we're not doing this kind of single-word answer reference lookup stuff. I'm also not the biggest fan of the "banal" in there, but frankly it's also the best way to describe that kind of unimportant trivia we don't care about. It's not like we don't care about minutiae at all. I explicitly ask the asker to motivate his question, though, which I think is an improvement over the eixting close-reasons, which don't actually present a way out, one that for many supposed "trivia" questions actually exists.
