Is the speaker responsible for the death of someone they disliked and prayed to be rid of, then wished for their death in a moment of anger, and that person died a few days later?

There is no harm in supplicating against a person that they be kept away from you merely due to dislike or disapproval of their actions, as long as it does not lead to sin or cutting off ties of kinship. However, supplicating for their death is not permissible unless their injustice towards you is clear and warrants a supplication for death; for Allah Almighty says: ﴿Allah does not like the public utterance of evil, except by one who has been wronged﴾. If the injustice is minor, it is not permissible to supplicate with something greater than it, otherwise, it would be an transgression. If there is no injustice at all, then supplicating against them and wishing for their death is injustice, aggression, and an transgression in supplication, and in this case, repentance and seeking forgiveness are obligatory.