This is a trait we've seen from only a handful of wrestlers in WWE's past, most prominently Kane and The Undertaker. The ability manifests in different ways but they both “control” lighting. 'The Big Red Machine' can magic trigger explosions and a sustained lighting change by slowly raising and then rapidly lowering his arms. Presumably it was originally done to intimidate foes or impress audiences but it's since become a way for Kane to express frustration or get a cheap pop as much as anything else.
‘The Phenom’ uses his light-controlling abilities to make grandiose entrances. That's developed over the years too. Eerie walks to the ring have always been a part of the character but they've become increasingly elaborate and drawn out. It’s important to note that a darkened arena has always been a part of ‘The Dead Man’s’ entrance. A key aspect that remains unchanged is that 'Taker raises the lights back up when stood on the corner steps. As with Kane he triggers this control by slowly raising his arms (what happens when he lowers them rapidly is unknown1).
In kayfabe terms these skills are clearly meant to be supernatural in origin. We can tell this from the body language of the performers and the way in which the lighting is addressed by the commentary squad. Also from the fact the The Undertaker and Kane both, in storyline terms, have supernatural origins. The lighting changes associated with, say, Sin Cara are contextually explainable as something being done in the production truck to mark out his matches as something special. That's clearly not what we're meant to assume with The Brothers of Destruction.
|He's doing magic!|
Which leaves us confused on the subject of Bray Wyatt. His entrance sees him walk through a darkened arena holding a lantern. When he blows that out the lights return to the arena. If you overlook the fact that extinguishing a flame triggering the return of full lighting makes no sense then it seems as though this is being presented as a magical power.
It's not as clear or obvious as with 'Taker and his bro, nor is it as impressive, but it seems to be what they're going for. The bottom line is that it's a wrestler controlling the lighting as part of his entrance. He may not have obviously supernatural kayfabe origins but it appears Bray Wyatt does have (kayfabe) magical powers.
1 A gateway to a parallel dimension is summoned perhaps?