Rejoicing at another's misfortune is "shamatat". Rasulullah 'sall-Allahu 'alaihi wa sal-lam' states in a hadith-i-sharif [1]: "Do not have 'shamatat' for a religious brother! If you have 'shamatat' then Allahu ta'ala will deliver him from the disaster and punish you with an identical disaster." It would not be "shamatat" if one feels happiness upon hearing the death of an oppressor due to the jubilation of deliverance from his oppression. Being happy upon hearing the disasters and troubles other than death one's enemy is suffering will be "shamatat". It will even be worse if one believes that one is the cause of the disasters and troubles, e.g., by supposing one's prayer (dua) has been accepted and so one's enemy is suffering. Such belief would cause one to catch the vice of self love ('ujb). One should think the suffering of one's enemy might be (divine) deception ("Makr" or "Istidraj") for oneself. Therefore, one should pray for the removal of those troubles. Rasulullah 'sall-Allahu 'alaihi wa sal-lam' states in a hadith-i-sharif: "A Mu'min's good prayer 'dua' on behalf of another Mu'min brother will be accepted. An angel will say, 'May Allahu ta'ala give the same goodness to you also!' And then they will say, Amin! Prayer 'dua' of an angel will not be rejected." If the enemy is a tyrant (zalim) and the disasters and troubles he suffers will prevent him from oppressing others, then being happy about his suffering over those troubles would not be "shamatat" and would not be a sin but instead it would be religious ghayrat. Religious ghayrat is an indication of firmness of one's belief. It is good to have ghayrat for Allahu ta'ala. It is not so good if it is due to one's bestial desires. In fact, being happy upon hearing of the suffering of the tyrant is not a good thing but since it prevents him from oppressing others, it has become permissible.

[1] hadith (sharif): i) a saying of the Prophet ('alaihi 's-salam).; al-Hadith ash-sharif: all the hadiths as a whole; ii) 'ilm al-hadith; iii) Books of the hadith ash-sharif. iv) Al-hadith al-qudsi, as-sahih, al-hasan: kinds of hadiths (for which, see Endless Bliss, II).