UPDATE: 
The YouTube recording was taken down sometime after 9:45 a.m. today.

But it wasn't because the academy demanded that. Rather, the academy ruled the video allowed under the service's rule which permits free exercise of religion. From the academy:

The Air Force Academy's goal is to foster a climate of respect. The Air Force has policies in place concerning what is and is not appropriate in regards to religious expression. These policies aim to balance the individual's right of religious expression with avoiding the appearance of inappropriate endorsement. 

When allegations are made about potential violations of these policies, they are thoroughly reviewed. 

Regarding the complaint concerning a cadet making an on-line video statement about his High School experience, his personal faith, and preparation for college; we have determined that the cadet's behavior is consistent with AFI 1-1, paragraph 2.11 and 2.12, Free Exercise of Religion and Religious Accommodation. [...]

When did Dinosaurs roam the planet?

According to Discovery News, which is described by the newspaper itself as "A publication of Significant Archeological Discoveries and Biblical Truths," dinosaurs and humans co-mingled on planet Earth.

This defies all scientific research, which has long concluded that dinosaurs went extinct some 65 millions year ago and that homo sapiens didn't emerge until about 200,000 years ago.

But Discovery News champions the co-existent theory to under cut evolution, citing on its website that a revelation that humans and dinosaurs lived at the same time would support the claim "that all species, including man, were created at one time."

What you read in your living room is your business, but when this kind of drivel is distributed at the Air Force Academy, it gets people's attention.

One retired Air Force officer encountered the publication during a visit to the academy's ophthalmology clinic and reported it to the Military Religious Freedom Foundation, saying:

Most distressing about this situation is that previously on two appointments I had ignored Christian proselytizing materials found there leaving them in situ, but this was just too much.

Here we have the “Discovery News”, that someone has placed in the waiting area, on top of the other magazines, with the obvious intent
that someone could be attracted to its colorful front page and then see a creationist set of ridiculous myths that through a series of contortionist pseudo-science set of disproven facts proves the bible is to be believed verbatim, that is through a series of cartoon panels that Jesus died for your sins.

I have never been so offended in my life and decided at that moment to pick this piece of silliness up and throw it away with the same fervor that it had been placed there. Who did put it there? Was it a member of the staff? Do the doctors of the 10th Medical Group all believe Earth is clearly less than 100,000 years old? I wanted to take this cartoonish piece of propaganda into the Doctors' office where my wife was being treated and ask the Doctor, “DO YOUR REALLY BELIEVE THIS?” And
then follow up with, “OK, then why do you allow it to be in your waiting room?”

Does Gen [Michelle] Johnson [academy superintendent] refute 100s of years of careful science and contort herself into allow the teaching of creationism in the USAF clinic because of fundamentalist evangelical Christian beliefs? 

The purpose of the visit was medical care, not a defense of the theory of evolution against creationism. I also worry we'd get treated differently if they knew we didn't share their same beliefs about the
world being created in six days and people and dinosaurs walked around together and (fill in the blank). That's why I'm coming to the MRFF.[...]

Email to MRFF From U.S. Air Force Academy Graduate, USAF Veteran and MRFF Client With Verified Complaint About Christian Proselytizing Materials left in the USAFA Ophthalmology Clinic:

From: USAF Veteran/MRFF Client
Subject: At the USAFA Clinic
Date: November 30, 2016 at 11:11:33 PM MST
To: Mikey Weinstein <[email protected]>

11/30/16

Dear MRFF,

The attached .pdf files (Link to PDF #1, Link to PDF #2) are the scans of the first and last
page of the “Discovery News” that someone left in the USAFA Ophthalmology
Clinic. I am writing as an Academy
Graduate, a retired 23+ year active duty officer, and a veteran. Most distressing about this situation is that
previously on two appointments I had ignored Christian proselytizing materials
found there leaving them in situ, but this was just too much.

Here we have the “Discovery News”, that someone has placed
in the waiting area, on top of the other magazines, with the obvious intent
that someone could be attracted to its colorful front page and then see a
creationist set of ridiculous myths that through a series of contortionist
pseudo-science set of disproven facts proves the bible is to be believed
verbatim, that is through a series of cartoon panels that Jesus died for your
sins. I have never been so offended in
my life and decided at that moment to pick this piece of silliness up and throw
it away with the same fervor that it had been placed there. Who did put it there? Was it a member of the staff? Do the doctors of the 10th Medical
Group all believe Earth is clearly less than 100,000 years old? I wanted to take this cartoonish piece of
propaganda into the Doctors’ office where my wife was being treated and ask the
Doctor, “DO YOUR REALLY BELIEVE THIS?” And
then follow up with, “OK, then why do you allow it to be in your waiting room?”
Does Gen Johnson refute 100s of years of careful science and contort herself
into allow the teaching of creationism in the USAF clinic because of
fundamentalist evangelical Christian beliefs?
I do not believe that is the case.
If I have to endure looking at this stuff or have the option of not
having the convenience of anything other than a bare table, I choose the
latter.

I did not confront the staff there. Maybe they didn’t try to sneak it in, and
maybe they’d be as disappointed as I was, and there was the fear I’d embarrass
my wife. The purpose of the visit was
medical care, not a defense of the theory of evolution against
creationism. I also worry we’d get
treated differently if they knew we didn’t share their same beliefs about the
world being created in six days and people and dinosaurs walked around together
and (fill in the blank). That's why I'm coming to the MRFF.

I suppose I’d be upset if there had been a Koran there or one of the sacred Hindu texts, but the point is I don’t
like the idea the USAFA is allowing this sort of stuff in the Clinic. At the very least, someone can walk through
there in the morning, straighten stuff up and throw this stuff away so I don’t
have to.

Grateful MRFF Client
Name Withheld

Email to U.S. Air Force Academy Superintendent Lt. Gen. Michelle Johnson From Mikey Weinstein on Behalf of USAFA Graduate's Verified Complaint:

From: Mikey Weinstein <[email protected]>
Subject: OFFICIAL MRFF COMPLAINT
Date: December 1, 2016 at 1:26:57 PM MST
To: Michelle D Lt Gen USAF USAFA USAFA/CC Johnson
Cc: Information Weinstein <[email protected]>

**LT. GEN. Michelle Johnson, the Military religious Freedom Foundation (MRFF) has received a VERIFIED complaint from a USAFA grad and retired USAF veteran regarding the placement of “Discovery News” pamphlets and other proselytizing materials in the patient waiting areas of the USAFA Medical Clinic. Please see the below. You as the USAFA commander are most senior leader there and, as such, YOU are ultimately responsible for all such matters. Allowing such materials to continually litter the premises with its fundamentalist Christian exceptionalism and anti-science messages, whilst concomitantly at mandatory patient waiting areas at the USAFA Medical Clinic, generates the clear impression of USAFA-endorsement and validation of such idiocy. Please see AFI 1-1, Section 2.12.

Thus, MRFF demands that you cleanse the USAFA Medical Clinic premises forthwith of such fundamentalist Christian, sectarian, anti-science drivel immediately and punish all those who are found to be responsible for allowing it to continually and unconstitutionally poison the environment there. Please advise MRFF when you have completed this Constitutionally required task. Thank you. Mikey Weinstein, Founder and President, MRFF