The thing that bothered me is that there was malice in the actions of the girl and that she had lost her temper, never a successful approach for training. If a bat is the only tool available at the time, there are other ways that it could have been used, in a cool, calm, collected manner. Would have been far more effective too.
Don't get me wrong, what I saw disturbed me, but I don't think it constitutes abuse. Abuse is defined as intentionally inflicting pain (which she did) beyond necessity for normal dicipline (herein lies the possiblity for interpretation).
All horses deserve, at least once in their lives, to be loved by a little girl.