This will become a little off-topic, but the topic itself is, too.
The camera's focal length is 24mm, which I understand to be relatively similar to the human eye
Focal length is only one of two parameters determining the field of view. In fact, for an object at given distance, it determines the size of its projection on a screen. For a simple, thin lens, sizes and distances (from the lens axis / lens) are given by
$$\frac{\text{object size}}{\text{object distance}}=\tan\alpha=\frac{\text{projection size}}{\text{projection distance}}$$
For objects far, far away, one can approximate $\text{projection distance}\approx\text{focal length}$.
So, the projection of the moon by a 24mm lens is just 0.22mm in diameter!
The second important parameter is the size of the image generating area. An expensive DSLR camera has an image sensor of 36x24mm, the cheaper ones (APS-C size sensor) 22x15mm, a mobile phone may be 5x4mm or smaller. Only on the phone sensor, the moon starts to become more than a small dot compared to the entire image, and due to all that megapixels, the image also has some details when zooming in.
Also the human eye has a high resolution, so you can see the details, but the brain also plays some tricks to let the moon appear larger than it is.
One can assume that the virtual image sensor of a 3D software also is in the order of 36mm, see next paragraph. 586
But the moon is not only tiny on the image, since a FullHD image has just 2 megapixels, there aren't even any details visible when zooming in.
A 24mm lens on a 36x22mm sensor gives a horizontal field of view of 73°, which is about the value of the human eye, as stated in the comments. But this value does not only determine the field of view, it also determines how "3D" the image is. A photo taken from larger distance with high focal length appears flat compared to low distance and low focal length. And images taken at very low focal distance feel like taken by a mouse. Now, those guys using 55" TVs as monitor on their desk would like to reduce the focal distance, because, well, they are like mice in front of that screen. So, this is the reason why many games allow to adjust this parameter. 896