The Pyromaniac perk, as it appeared in Fallout 3, affected all Flamer variants, as well as the Shishkebab and the Firelancer. In New Vegas it was a little more diverse, also affecting a number of thrown weapons, two unarmed weapons, and three types of ammo. From what I can tell, there does not appear to be an icon on the chart that would relate exclusively to this idea. In fact, the closest match would be the one identified as Explosives.
What I believe is that, as we advance in ranks for the Explosives skill, we will be able to craft unique and progressively more powerful explosive devices, including incendiary ones. This skill would also increase, at least to a degree, the base damage from existing explosives such as mines or grenades. Other weapons that may be fire based, including Unarmed, Melee, or Flamers, would be improved via weapon mods. Note that Flamers would be modded using the Gun Nut skill, whereas unarmed and melee weapons do not require any crafting skill. This should not be an issue however, as the most powerful fire based weapons (other than incendiary devices), and therefore the ones most likely to be affected here, would be Flamers.
EDIT: unique fire based weapons such as the Shishkebab or Firelancer would almost certainly be given a higher starting damage to compensate for this.
I've actually been going over this quite a bit in my head, and something about my suggestion doesn't quite feel right.
In the gameinformer article, the only reference made literally says "something called V.A.N.S." This means that, at the moment at least, it could be interpreted in many different ways. And so, just because my idea "fits", doesn't mean it's right.
The reasoning behind my suggestion, as I explained in the OP, was the lack of any really solid stealth mechanic in previous Fallout games. And so I came up with the idea that a variety of existing elements from both Skyrim and Fallout 3 (both developed by BGS) could be wrapped up into one 'master level' perk such as the one I described. Oddly enough, this idea would still fit perfectly well even if we used a different name. Taking inspiration from the previous Ninja perk, as Leprechaun even hinted at in his thread, the 4 stealth options described could be grouped together as the 4 ranks of a brand new perk called Ninja Master. The difference in name here is important in the same way that Science! (Fallout 4) can be differentiated from Science (Fallout 3).
And so, looking again at the 4 ranks in this new, slightly different context, you would have the following:
Rank 1 would reduce noise from running or walking by half, like an advanced version of Muffled Movement from Skyrim. This would fit well alongside the Sneak skill, which would be more focused on remaining unseen, specifically when either moving in sneak mode or picking pockets. Rank 2 would eliminate all noise from running or walking, and would be the equivalent of the previous Silent Running perk. Rank 3 would allow us to throw our voice in order to confuse or distract enemies, in a similar way to how the Throw Voice dragon shout worked in Skyrim. And finally, Rank 4 would allow us to carry out a Silent Takedown similar to the Knockdown effect seen in both franchises. This would essentially mean that any successful melee or unarmed sneak attack that does not kill an opponent will render them unconscious. This would allow us, for the first time ever, to have an effective non-lethal takedown option in a Fallout game. This would be very useful if there were unarmed enemies (such as scientists at the Institute) who could notify others to our whereabouts. And so we could sneak behind them and knock them unconscious with the butt of our rifle.
And so this leaves us with something of a dilemma. We must find somewhere else to place V.A.N.S., and it has to be something that fits with the other perks, is completely unique, and also matches what we know about our protagonist and the setting.
Looking at my previous V.A.N.S. suggestion of Vocal & Acoustic Noise Suppression, this now seems more than a little too scientific. And besides, the Ninja Master perk explains exactly the same functionality in a way that makes a lot more sense, is easier to understand, and also sounds a lot cooler to boot. If we now look again at my suggestion for the Submariner perk, we can see that the icon shows Vault Boy standing inside a Moon Pool, the same type that are used in diving support vessels in conjunction with a variety of applications, one of which is underwater exploration.
If you look very carefully at the E3 footage https://www.youtube.com/watch?v=D5esyZPt5Jo&feature=youtu.be&t=3m40s at around 3:40, note the greenish image on the left hand side of the screen. Now watch this image as the footage progresses over the next couple of seconds. As the central image moves to the right, we see what looks like the HUD of an underwater vehicle of some kind, or at the very least a HUD overlay used to assist underwater navigation. This very subtle clue was actually first pointed out by Helljumper in http://www.gamesas.com/topic/1526246-the-glowing-sea/?p=24151698 post. Putting this all together, and seeing as we already have a Navigation system in the form of a map, compass, and objective markers, the next available option, which would perfectly fit the setting of the game is:
Vault-Tec Assisted Nautical System.
This perk, which fits with the image of VB described above, would allow us to activate an Underwater Exploration mode in the Pip-Boy, complete with a unique HUD as seen in the concept art image. We would then have a specific duration to be able to survive without oxygen (hence the perk being listed under Endurance), which would increase as our rank in the perk increases. With the higher ranks, we may also be able to unlock additional features, such as a weapons system. As a final observation, this explanation not only ties in with the concept of Vault 111 as described http://www.gamesas.com/topic/1523172-is-vault-111-built-like-a-submarine, but it also matches the Captain Nemo references I pointed out some time ago in http://www.gamesas.com/topic/1524192-more-clues-in-the-concept-art thread.
EDIT 1: the sneak skill as described above would also affect sound, but this would be limited to sound made whilst in sneak mode, and not when walking or running.
EDIT 2: the above explanation of the V.A.N.S. system would also give vault inhabitants a means of using the fail-safe escape tunnel built under the vault, as explained in the linked thread! This tunnel would be reached via a decompression chamber containing a Moon Pool as shown in the icon for the perk. This would then lead us out through a subterranean tunnel and into a nearby lake where we could escape, if the main exit to the vault had become blocked. This is the route that I have suggested the Institute took when accessing the vault.