Good questions. (Which reinforce my intuitoin that Emerikol would classify this as a "dissociated" power.)If you mixed that with blindness (probably need to dip into 3E for true blindness), or with a necromancer's skeleton (mindless), or if a player puts on a blindfold deliberately to (try to) avoid the effect, what happens? (Perhaps 4E has creatures with immunity to fear because of their nature, so the skeleton example may or may not work.)
Probably, blindness won't work, since the "Visage" implication of a visual effect is not correct. Maybe there is a sound effect, too, but that doesn't matter either. The practical details of effect make it most similar to a purely psychic effect such as an Illithid mind blast. But then, why doesn't the power have [Fear, Psychic]? Does the power work entirely through the senses, partly through the senses and partly on the psychic level, or entirely on the psychic level?
I think it probably should be psychic damage, with the [psychic] keyword, and the failure to stat it up that way is just an error or an oversight.
On the question about [fear] effects and skeletons, that goes to who has what sorts of immunities. These are scarcer in 4e than 3E, but a mindless skeleton could in principle be immune to fear and/or have psychic resistance.
I think the most interesting question is how, if at all, a blindfold, earplugs etc help. The game leaves this up to the GM to adjudicate. It is not a [gaze] attack, so blindness does not automatically provide immunity, but I think it would be reasonable to have it give the Wight a penalty to attack (-2 is the default circumstance penalty in 4e). This requires the GM and the player to be ready to negotiate some fictional details on the run. My personal view is that 4e's otherwise fairly robust maths helps with this, by giving the player confidence that what is at stake is a meaningful adjustment to what is, nevertheless, a basically mechanically fair starting point, rather than the PC's life or death turning on the GM's arbitration of the situation.