Considering Reese is 6 feet tall and he is probably close to 2 body lengths from the goal plus you add a foot or two on the distance of his stick he probably is pretty close to 14 feet away.
To me it looks like they're measuring the travel distance from where the puck was shot to where it crosses the goal line.
The pinnacle of the crease is only 6 feet out from the goal line, from where the curve of the crease ends to the goal line is 4 feet 6 inches. Without the overhead angle of the net it'd be hard to get an accurate point for where the puck was shot from because we don't have the angle that the camera is located relative to the ice surface.
That said, I'd say that's about a foot and a half outside of the shortest part of the crease when the puck is directed towards the net. I think if we were calculating the shortest route the puck could take to pass the goal line it would probably only be around 6-7 feet out.
I think that's the key difference, they're measuring the total travel distance from when the puck was shot (probably accurate around 12-14 feet in the Zach Aston-Reese goal) rather than the shortest distance to the goal line from where the puck was shot. It won't be a big deal for most goals, but anything that goes behind the back of the goaltender and goes in perpendicular to the face of the goal might end up with a longer travel distance and make tap-in goals appear as if they're 6-10 feet out.
The Johansen goal is a little more egregious to me because I think it was basically put in from the goal line rather than the 9 feet recorded. 9 feet would probably be accurate if they were measuring from the initial shot, but it looks like it was the poke that puts it in from under Holtby.
The Mantha goal throws a wrench into my travel distance theory though, because that was tapped in from probably a foot out. A single foot out is a far cry from the 6 feet it was recorded at, unless they're recording body position rather than puck.
Frame 1 shows where the puck ends up after the initial save on Larkin's shot, Mantha hasn't touched the puck yet at this point.
Frame 2 shows the location of the puck when Mantha directs it into the net, Mantha's closest skate is around 6 feet from the goal line at that point.
Regardless of what's going on here, the NHL probably needs to explain the inconsistency.