We did not vote Gore or Hillary into office. They got more popular votes and lost in electoral votes, and only electoral votes count for president. They lost fair and square, in the system we have.
No the difference between republics and monarchies is not “talking about assassinating rivals.” You can say anything, that is anyone’s right. In the context from above, this difference is why political assassination is not acceptable in a republic. It would be insane to say that political assassination is OK if the person had ever talked about assassinating rivals. The penalty for distasteful speech is not death.