Could a structure similar to that shown in the image below inspired by Roger Dean’s “Close to the edge” actually exist in nature? If not could it be constructed artificially and if so how? Assume the two bodies of water obscured by the mountain on the right terminate in waterfalls and that the waterfalls run constantly at high volume.
Yes, this is strictly a matter of size. You need a massive influx of water from rain, which is proportional to the surface (goes roughly with the radius squared), while the waterfalls outflux is proportional to the circumference of the plateau.
When the radius is large enough, you can get enough water to feed all the waterfalls. In nature however you'll get some waterfalls to erode faster than the others, lowering the water level, so that you don't really get a continuous range of waterfalls; given long enough, "there will be only one".
So you need a maintenance mechanism that counteracts the erosive effect (which for waterfalls is huge - I heard that the Garganta del Diablo falls back half a meter every year, or something like that).
You could posit some kind of reef coral able to grow and counteract the erosion; the coral cannot live outside the water, and it thrives at the brim due to the influx of oxygen and food particles, so it only reaches up to the brim, reinforcing it. Also possibly imperceptibly raising it over the centuries, so that the plateau slowly becomes a "cup". The effect is self-limiting, because if the coral grows too much, the waterfall slows down, oxygen and food become scarcer, the coral begins to die and the "waterfall-less" area crumbles, restoring the waterfall at that point.
Taking a rain check
We cannot have too large a plateau because we need to get humid winds all over it, and there are no plausible mechanisms that allow this on a Earth-sized planet, constantly and for very long distances.
Also, as @Braydon correctly pointed out, if we have a moon, or the same strong winds that feed rain to the plateau, they'll start interacting with the water surface and disrupt the waterfalls.
So let's try to come up with a size estimate for the plateau.
It needs a lot of rain. On Earth a plausible "lot of rain" (monsonic rain) is around 120mm/die in multiple daily or nightly showers (I witnessed a 250mm/hour downpour and was quite shocked, but survived).
A waterfall rate like Niagara is 2500 cubic meters per second over 1200 meters of aperture. Let's approximate it to F = 2 cubic meter per second per meter of aperture.
The available water daily rate is 12cm, approximated in P = 1/8 cubic meter per square meter. Every eight square meters of surface we have, give us one cubic meter each day and no more.
One day contains 86400 seconds, so every meter of the circumference requires F*86400 m3 of water, which means we need F/P*86400 m2 of surface to sustain each meter of circumference.
So it must be true that (imagining the plateau as circular) surface $\pi r^2$ is F/P*86400 times the circumference $2\pi r$. With F=2 and P=1/8, F/P is 16.
$\pi r^2 = F/P*2*86400\pi r$ means a minimum radius of r = 2764800 m, or 2800 km, and a surface of 24 million square kilometers - more than three times the size of Australia.
In short, $r = 17280*F/P$ with r in kilometers, F in cubic meters per meter of aperture, and P as centimeters of rain per day.
By reducing F or increasing P, the surface can be reduced. For example halving the flow to half of that of Niagara, F = 1 m3/s per meter, the surface is reduced by a factor 4.
A still respectable waterfall is about 0.3 m3 per meter, and this would allow us to reduce the radius by a factor of six (the surface by about forty times), to "only" 470 km.
Remaining with the original figure of 2800 km, there would be another thing that's not really going to fly - where is the rain coming from? That precipitation rate is an average, but it's not likely that in the center of the plateau, 2800 km from the border, there's a significant inflow of humid air; all rain brought by the wind ought to have fallen in the first 2800 km, and actually one has to wonder what the clouds and the winds at the border must look like.
Actually, it stands to reason that if the wind need to arrive 2800 km inland in one day, it has to travel at almost hurricane speed, always.
So we're talking about a planetary-sized permanent hurricane - something like the Great Red Spot on Jupiter.
The same formulas work if we suppose that there's constant heavy rainfall near the border and more bearable weather further inland, provided the average rate stays the same. Which means, the drier the center, the more abysmal the conditions on the boundary.
This is very similar to the OPs other question
except not exactly the same. So I suppose it should remain different so someone does not say OP is asking too much at once.
There is not a spring up there. The tops of tepuis get a lot of rain. If you had a really big one it could be enough rain to get a near circumferential waterfall. I suspect over time though the water would find the path of least resistance and you would wind up with one big waterfall. Although waterfalls can be very wide. This Chutes Wagenia (not on a tepui!) is 4500 feet across; well over a mile.
As mentioned by slarty in the comments of another answer, this could be managed through siphoning from a higher reservoir. This was mentioned as an artificial method, but siphons are also expected to form naturally. Although it would take some stretches for a large enough one to both form naturally and be made of hard enough rock to not be very quickly eroded by such a high flow rate.
Possibly a tuya would provide a good solution. Solid igneous rock would resist erosion and may justifiably have a series of lava tubes for the siphon. Glaciation would also lead to deep valleys which might justifiably be dammed up naturally, leading to the required high reservoir for input. This natural damming could also justify this waterfall being geologically recent so the erosion is not as much of an issue.
No, it can't appear in nature because there is no addition of new water, and as the water falls off at the water falls, it is not replenished. The only way to achieve this would be with a colossal pump under the lake pushing up massive quantities of water, basically making it a colossal fountain.
If you want something naturally occurring and similar, the most similar scenario would be that it has a higher cliff face on one edge from which more water pours down, replenishing the waterfalls. You would also likely need to town back the water falls.