It does have me at least confused.
There is a class of chemicals and minerals that are deemed essential. Vitamin B12, Vitamin A and so forth. And minerals like Calcium, Copper and Zinc, just to name a few.
And then there are many chemicals that seem to aid greatly in human nutrition. I will simply mention Lutein for the eyes, as one. But they are not classified as vitamins.
Why didn’t they make the list?
Vitamins are organic compounds that are micronutrients - needed by the body in very small quantities, but substances the body cannot itself create. It is not actually clear that the body needs lutein so it didn’t get into the club. If it is discovered to be essential maybe they’ll make it a vitamin.
Calcium, copper and zinc are inorganic, so are not vitamins.
Fat, carbs, and proteins are not micronutrients - you need a lot of them - so also aren’t vitamins.
Betty’s not a vitamin, either. 
http://www.bettysnotavitamin.com/
Apparently, the band got its name because Betty Rubble was not originally included in Flintstones vitamins. I actually liked the name better before I knew that.
IIRC, vitamins are essentially metabolic catalysts…modifying the rate of metabolic chemical reactions in the body, without the catalysts themselves being “used up” in the reaction.
Lutein seems to be a straightforward protein, utilized by the body as a structural and functional framework within the retina.
If I may offer a bit of possibly wild-ass comment, based on something I thought I learned as a young child in school:
I was under the impression that Vitamin A, Vitamins B, etc., were so called because their existence was realized before scientists had any idea of the actual chemistry involved. Thus, they were known, but mysterious, before they were understood. So they were given the generic-sounding names (rather like the “placeholder names” given to trans-100 atomic elements) rather than proper chemical names.
As chemists and nutritionists came to understand the chemistry of vitamins, the chemicals were given more proper chemical names (e.g., niacin, riboflavin, etc.)
So as more micronutrients have been recognized later, my guess would be that they get chemical names from the start instead of generic “Vitamin” names.
Can anyone with more knowledge tell if this theory is consistent with the actual history of vitamins?
ETA to the above: Also, so-called “vitamins” (A, Bx, C, etc.) are so-named or categorized according to the function they perform for the body’s nutritional needs. And a particular “vitamin” is not necessarily exactly one chemical – for some vitamins, there may be several different (though similar) chemicals that will do the job.
For example, three different chemicals, pyridoxine, pyridoxal, and pyridoxamine, all can function as “Vitamin B6”, and similarly, there are a variety of chemicals that are all “Vitamin D”.
The word vitamin is interesting as well. Supposedly originally a contraction of vital amine. However not all vitamins are amines, so we ignore that bit of history. There is some curiosity in the names too. Vitamin C is often given the name ascorbic acid. Which sounds nice and technical and chemical until one realises that the name is a-scorbic - that is something that is antidotal to the dreaded scorby, aka scurvy.
Overall I think it is fair to say that modern biology has moved on past the idea of vitamins as a special class. We would have long run out of letters.
No one has yet found an essential role for lutein in retina or elsewhere. That’s required before something can be called a vitamin. There may be two dozen different carotenoids that can fulfill the same, unknown function.
@Senegoid your theory is roughly how I thought of it as well.
Al Capp, cartoonist of Li’l Abner, once had a strip showing Hairless Joe and Lonesome Polecat brewing up a batch of their trademark Kickapoo Joy Juice in a big cauldron over a fire, as they tossed various ingredients in. One ingredient was a horse, “to give it body”. The next ingredient was a typewriter, “for vitamins A through Z”.
When I first learned of vitamins (circa 4th grade or so?), I didn’t even get the concept that they were actually chemicals. I thought that vitamins were just some abstract quality or essence in foods, without any concept that they were actually chemicals.
I had no idea of this and it’s fascinating to me.
Googling around for examples, I found choline, which “…while closely related to the B complex family of vitamins, is not truely considered a vitamin since researchers cannot agree on any common definitions of deficiency symptoms”. 
(cite)
The software engineer in me is pained by the existence of a naming convention that could potentially be useful (it would be nice to be able to trivially list off all the known essential organic micronutrients by just running through A, B, C, …) but right now is inconsistent and not being added to.
I didn’t realise that niacin was short for “nicotinic acid vitamin”.