No, it's nothing wrong with the English definition of the assassinate/assassination. Btw, you aren't in a position to determinate the definition of English words. One more thing. there aren't any differences legally between the words murder, kill, and/or assassinate. The courts regardless country will treat the offender in the same way. The sentencing will be different if the offender has planned to murder/kill/assassinate somebody or if the offender did it in the heat of the moment. The majority of the homicides around the world occur in the heat of the moment.
This thread explains a lot when you have your own definition of words. Ask your mom about the definitions of words before saying something.
There are no first degree murders in Germany ( and the Israeli athletes were murdered in Germany, not in the USA ),thus : why are you talking about first degree murder, why are you using the Oxford/Cambridge / Collins dictionary ?These have no place in Germany or in the Middle East .
A court in Europe will laugh at a lawyer who will talk about first,second or third degree murder .