If someone is aggrieved, is the correct term for the party who made them so "aggriever"? If not, then what term should be used?
If by “aggrieved” you mean “wronged,” then the actor is a “wrongdoer.”
You would probably need to look at the type of wrong done to get a better word though, since many English nouns are based off of the verbs the correspond to (theft-thieve, murder-murderer, tort-tortfeasor, heresy-heretic, etc.)
For the one who spoils the pleasure of others, you may generally use killjoy and spoilsport. More specifically, for the one who exudes depression or sadness and thus dampens a light or happy atmosphere, there's a term wet blanket. And someone who refuses to go along with everyone else, may be called a party pooper or just a pooper (the one who poops out on an activity); although the latter is marked as vulgar, so one should be careful using it
Suppose that Al and Betty have an interaction.
Later on, suppose that Jim convinces Betty that she should be angry at Al about the interaction. Perhaps Jim convinces Betty to condemn or complain about what Al did. Then Jim is a "grievance monger". If Jim went around telling people about Al's and Betty's interaction, then he is also a "gossip" or "gossipper".
If Al really was in the wrong (especially if he broke a law), then he is an "offender". But it is also possible that Al was in the right, or that neither Al nor Betty did anything wrong.