5984.3 Assessment
Research Question (Clear, unambiguous) The suggestion that "people who have been bullied as a child will have a higher emotional intelligence than those who haven’t" seems unconvincing at best.  The idea that emotional trauma sharpens one's emotional "skills" seems psychologically odd.  It is also difficult to reconcile the later statement that if "negative effects keep following a person into adulthood, then it may in fact leave an adult emotionally-stunted, keeping them from ever reflecting on their experiences and understanding others."
Relevant Literature While the psychological literature on bullying seems mildly relevant, the problematic idea of "emotional intelligence" and literature on life histories seem neglected here.
Causal Interpretations (clear, all parts defined, mechanisms, controls, plausible) The discussion of causal interpretations seems vague.  The only mechanisms are vague notions that childhood bullying might have adult effects - it might, but so might anything else.  Being bullied is also not a random even, so you would have to have a reasonable causal model of becoming a bullying victim so that it is possible to control for those circumstances, as they are obvious likely causes of adult effects.
Data (variables, sample, comparison) The data choice seems okay for looking at the adult effects of childhood bullying.  The data do not seem to offer much to operationalize the already vague notion of emotional intelligence.  
Research Value Beyond some possible therapeutic agenda, the point of the research is a bit obscure.  The idea that bullying victims might draw comfort from a theory that bullying could have some positive personality effect - a version of the trope that what does not kill us makes us stronger - seems silly.
Overall Frankly, a doubtful venture as portrayed here.