Does Allah Almighty’s saying: "And We ordained for them therein a life for a life, and an eye for an eye, and a nose for a nose, and an ear for an ear, and a tooth for a tooth, and for wounds is legal retribution" mean that the injured party must retaliate against the aggressor in the same manner of harm? For example, if something was stolen from him, must he steal from the thief?

Retribution against an oppressor is permissible, not obligatory. One can pardon and forgive him, as stated in the Almighty's words: {But whoever remits it, it shall be an expiation for him}. It is not obligatory, and indeed, it is not permissible to take money from someone who stole from you. However, if it is possible to take the equivalent amount of the stolen money without it being attributed to theft, scholars have differed on the permissibility of that.