Well, not really, but it looks like the fittings were supplied by the plumber.

When are these required?

Looks like someone's creation to buffer vibration from the conduit run or possibly for expansion/contraction....

I've seen the rubber ones used in bridges. Normally for seismic joints FMC or LTFMC is used.

Maybe using these is cheaper than LTFMC for machinery vibration.

Those are called "deflection couplings". They're used when the conduit on one side may end up misaligned with the other due to movement or vibration. You can find them in the Appleton catalog.

How does the conduit stay bonded with these?

Probably bonding is accomplished with a flexible braid or strap.

Here is some more info on them.
http://www.appletonelec.com/pdf/DeflecandExpan.pdf

They look like the technology developed by the USAF for ICBM and command bunkers for nuclear war.

In such systems, everything -- I mean everything -- is on flexi-mounts so as to work after a Richter 15 earthquake.

Specified normally in government contracts only.

Nick,
I'm not surprised that you recognize these!

This is insisde the parking structure at Treasure Island, Las Vegas......One of your little projects.