I think it's just "for dramatic effect".
It's an indicator of where the next important action is going to happen, to the audience, via Jon's character.
We see the Night King looking out to Jon on the boat; close his eyes, turn his head, then look out over the devastation in Hardhome. We then get a Jon [almost] POV* shot of where the Night King is looking - that's movie-speak for "I'm looking at what you're indicating I should look at". A brief shot of Jon looking back at the Night King, as he turns back to face Jon, plus a couple of back and forth cuts for a tension builder… then the moment of resurrection.
The resurrection itself begins in cut-aways to blue-eyed close-ups, before moving out to POV again; always inter-cutting to Jon's reaction, until we cut back to Karsi then again the Night King . One more POV and we see them rowing away - defeated - against an increasingly-wide backdrop of Hardhome post-resurrection. A sign of things to come… and fade to black.
*Jon's POV [point of view] shots all actually include Jon in the shot, close and out of focus, so they're not "true" POVs, but they serve the same purpose - we see 'what Jon is looking at', giving the audience the clue as to also know to look there for the next plot point.
GoT is very cleverly shot, but it does include these 'obvious' audience pointers so we can keep up with what's about to happen. They do like the 'fast cut' setups, flipping from character interplay, to close detail, to scenic wides - all so we know where the action is taking place as well as being able to see detail of it.