For a misdemeanor (as the shoplifting described in this case appears to be), only if the arrested party actually committed the offense and it occurred in the arresting party’s presence (for a felony, the terms are somewhat looser.)
As the description clearly indicates that the offense did not occur in the poster’s presence and he wasn’t even aware of the offense until after using force to restrain his victim, he committed both battery and false imprisonment by violence, the latter of which is a felony offense, and the former is at a minimum a violent misdemeanor.