AT1's interpretation is pretty good.
The absence of nearby vessels is almost certainly a consequence of a day shape signal which either declares that the vessel is manoeuvring with difficulty or is "not under command". All ships will see that signal either by day, in the form of a ball over a double cone (diamond shape) over a ball, or by red/white/red vertically arranged lights at night and will give her a wide berth. There are variations on that theme, such as "engaged in underwater operations", but the message is pretty much the same: please push off out of my way. Furthermore the ships watchkeepers on the bridge will be watching any traffic within a dozen or more miles on radar and will call them on CH16 marine VHF (similar to 121.5) and request that they stay well away.
If the vessel appears to be almost stationary on AIS then one interpretation might be that she has deployed her ROV.
The way that works is that the ship maintains station on the ROV at a predetermined number of metres laterally and longitudinally from the ROV in "follow sub" mode and the ROV therefore controls the ship. It's quite cumbersome as the ROV is the size and weight of a Ford Transit or Galaxy and the ship weighs several thousand tons. The ROV therefore has to manoeuvre very gingerly and avoid making suddenly turns or accelerations. If the ship has to make very large thruster inputs to try to maintain station you can get aeration of the water under the ship which can cause loss of acoustic contact with the ROV and a massive muddle ensues. Angry words are exchanged on the intercom between the bridge and the ROV control shack. That's another reason why the bridge will want all other vessels to stay well away, preferably at least a mile or two.
It may perhaps interest Prooners unfamiliar with how these things work for me to explain a little about underwater nav.
There are two principal methods. Long baseline and (ultra) short baseline.
USBL works in one of two different modes. The first involves the ship sending out an interrogation pulse from a transducer which extends below the hull telescopically rather like a military submarine's periscope, only in the opposite direction. The ROV has a transponder which waits a known number of milliseconds and transmits a reply pulse. The ship's USBL transducer is a small cruciform affair and by measuring the phase difference at the four transducers you derive the angle at which the pulse arrived. Thus you get a 3-D position with respect to the ship. The other USBL mode involves sending the interrogation pulse electrically down the umbilical and a "flowerpot" responder on the ROV replies with a pulse just like a transponder. Advantage is that the interrogation is almost instant and not prone to raypath anomolies or acoustic noise on the outbound signal.
Long baseline is completely different. It involves setting out an array of seabed transponders and co-ordinating them. The ROV then self-navigates by doing what amounts to a DME/DME fix, using at least three and preferably four or five transponders. It then telemets its self computed position up the umbilical. Much more practical for deep water work like this job than USBL which will be slow and wooly. I'd be adversely surprised if these guys haven't deployed an LBL array around the locus by now.