Is expiation (kaffarah) obligatory for one who swore not to return to gambling, then invoked harm upon himself if he were to return to gambling, and this was done in a state of extreme anger?

Anger does not prevent an oath from being binding as long as the swearer's intellect remains intact and he understands what he is saying. If the oath was binding and you broke it, then the expiation for breaking an oath becomes obligatory upon you. Fasting in this case is only permissible after being unable to feed, clothe, or free a slave. As for a supplication uttered in a moment of distress or anger without genuinely intending its meaning, it is hoped that it will not be answered.