Is a REPLAY POINT soley the subjective decision of the Chair Umpire?

It is the umpire's best judgement whether the ball was playable or not. It sounds like they were wrong in this case. Sometimes if a player thinks the ball was out though they give a half-hearted effort and it makes it look like the shot was better than it was. Didn't see the point in question, but there's really no better way to do it unless you just replay every questioned point and that doesn't make sense either.