Just to elaborate on my post above. I'm not advocating a retake in the absence of an appeal. Like awarding a PK without VAR to validate a decision, I would strongly discourage any referee from being clever enough to be the only person in the ground to see an incident. But once an appeal occurs, any advantage gained (save made) from being off the line must be penalised as it is an extremely important KMI and what we're paid to adjudicate on. Any other mentality fits into the insidious disease of excessively safe refereeing that contributes to substandard refereeing at all levels. I learn a lot about a Referee when they mention 'needing to be on the halfway line, or we're not having re-takes' during the pre-match discussion. This mentality is weak and needs eradicating in my typically strong opinion.
I've had two retakes in my time and both were warranted and respected. There is nothing to fear when an appeal occurs and the decision is correct.
Nor do I see a need for incognito communication between AR and R. I believe the AR should give the decision and they should get their bloody flag up and stop hiding. That is, assuming the Ref is confident enough in his/er ARs and gives them that responsibility in pre-match. This responsibility must be discussed in pre-match
FWIW, the GK in the OP is only slightly off the line when the ball was kicked, but it should have been a retake nonetheless. The way the AR slaloms back to the touchline looks amateurish although getting back to where you need to be in such circumstances does require teletransportation