In Alabama, an individual may effect a citizen's arrest for any offense committed in his presence or for any felony, whether or not it was committed in his presence. Kicking a child in the head is a felony. If the perpetrator resists arrest, force may be used to stop that resistance. If the perp continues to resist, there will be escalation. Therefore, the arrestor can justifiably (under both self-defense laws and citizen's arrest laws) escalate the level of force he uses to a reasonable level to overcome the level of force from the BG.
It is possible (not likely, but possible) that the escalation proceeds to the point where the arrestor feels that life or limb is in danger. Under AL self-defense law, he may use deadly force to protect his life or limb.
In the case at hand, the level of force used by the arrestor was not an unreasonable response to both the attempt by the suspected felon to flee the scene and his attempted use of force to do so.
(BTW, the citizen's arrest scenarios have been discussed extensively at ALOC with citations of the relevant AL laws. One quirk of AL law is that it is not unlawful to resist a citizen's arrest, which could result in lawful escalation from both parties until someone ends up lawfully dead. This case would be one just like was discussed: A felony was committed outside the view of the arrestor and was over by the time the arrest was effected. The arrestor could legally use force. The perp could claim self-defense in responding to that force. Rinse. Repeat. The cycle stops when the BG stops resisting, the arrestor gives up, or someone dies--lawfully.)