What is the object moving across the ceiling in this stock footage?

The clip looks like it's from a movie, carefully framed to show this exotic looking gizmo. I think it's a movie effect.

The large diameter transparent tube with no visible supports or joints is unlike any pneumatic tube system I can find depicted. Also the diameter of the tube is much larger than the capsule, implying it has unreasonably thick walls.

I must respectfully disagree with existing answers to this interesting question.

As Keith McClary noted, this object has a larger diameter than most pneumatic capsules. Capsules have reason to be small, both to increase pressure per area on their exposed surface, and so that tubes with wide bends can fit into buildings. According to an archived article from capsu.org, "Most tubes were 2 1/2 inches in diameter, with 3 inch diameter tubes being used where traffic was particularly heavy." What is shown in the video may be a foot in a diameter.

No tube at all is visible here. Rather, the mystery object rides atop a thick, rigid rail, casting a tight shadow upwards which might otherwise be distorted by the light passing through a glass pipe. This rail's hanger therefore has to be offset to avoid fouling the payload. Despite the camera's movement, the hanger visible at the right seems to consist of a single L-shaped element. No tube would be hung in this fashion.

Wikipedia suggests a normal speed of 7.5 to 10 meters per second for pneumatic capsules. The object in the video is moving not much faster than the men walk, or maybe a tenth of a capsule's speed.

The "MATTEL, INC." stock certificate that follows is a good clue that could lead to a precise answer. While Mattel is a toy company, the object is not obviously a toy, though it could be a prototype of one.

The object is used for some kind of transit but as we do not recognize its form, it is probably a purpose-built container of specific dimension, a shuttle borne along the rail by a chain drive or worm drive system.

That's a pneumatic tube. The tube itself is transparent in this case, but the object you see moving through it is a capsule carrying documents, or maybe cash or other small objects. They are still used in some places (in that link, for delivering food), but were a common feature of most offices before the rise of computers and digital technology.

Confirming Brian Z and his answer: this is most likely a penumatic tube mail system. And strictly speaking: "What is the object moving…?" – It's not a "cuboid box" but a cylindrical container, also called capsule.

Most easily visible in this still:

You see a darker edge on top, a lighter reflection of light at the bottom of the tube. On the right is a hanging fixture for the tube extending right to the bottom of the loghter reflection. It's really everywhere, but more pronounced to the right of the head:
you also see colour variations of the ceiling as the light passes through the tube. This is most visible to the left, where the lights appear lens-like distorted. Also, the darker upper edge extends from phase change lighting extends all the way across the picture. Tubes vary in size and can (now) take 50kg.

This is not a rail bound system: The "darkening" is not just the obvious shadow above the box/capsule. The colour isn't uniform across the whole tube. That is clearly independent from lighting the capsule. Reflections on a possible rail at the bottom are one thing, but that colour variation along the entire picture gives it away. The distortion of lights left of the pillar and the gradient from the tube to the right of the second head are incompatible with just "rail". These would need explanation, not capsule/box forms.

Exaggerated:

In case the verbal descriptions are insufficient: only the glistening "rail" speaks for a rail system. But it is the lower edge of the tube, as these numerous hints would confirm, which a "rail" cannot explain:

Especially the last few frames to the right make the tube quite obvious.

These are still in use today.

Not only thinks the German State Minister for Digitization that these are still indispensible.

They also look cool:

Source: The Pneumatic Tube System (PTS)

For a size comparison of possible systems, roughly "from that era":

_{A look at what’s left of NYC’s pneumatic tubes Surprisingly, some buildings still boast functioning pneumatic systems June 07, 2015 05:00PM and Pneumatic Tubes In New York City}

And they could be a bit larger still:

The Pneumatic Despatch

The London pneumatic tube mail train at its formative stage!

More variety:

^{src: Pneumatic tubes}

^{src: Pneumatic Tube Systems: Spare Parts, Service and Support}

^{src: Society Adventures: Exploring Stanford Hospital’s Pneumatic Tube System}

^{src: Pneumatic Tube System / Carriers}

^{src: Pneumatic sample transport}

^{Image: Photograph Showing An Operator Preparing To Feed A Carrier Holding About 500 Letters Into The Transmitter For Despatch Through The Tube From Brooklyn Post Office To New York General Post Office C 1899 ((Sspl/Getty Images))}

^{Distroller Wərld Opens Los Angeles Flagship Store}