John Wick agreed to kill Winston to reverse his ex-communicado status in *Chapter 3 - Parabellum*, and to reaffirm this, cut off his finger for the Elder, yet when presented with the choice, he chooses not to kill Winston, which as I see, renders him cutting off his finger was for nothing. is that correct?

The adjucator acts on behalf of the High Table, and deconsecrates the Continental in New York City. This basically opens up Winston's, Charon's, John's, and his dog's life to the mercenaries sent on behalf of the High Table. 

So what I don't understand is why John can't just kill the adjudicator? 

It's not like he's waiting to re-negotiate with the High Table or strike a deal with the adjudicator, and it's not clear if he knows what Winston plans to do. He's already marked for death globally, and the deal to re-consecrate the Continental doesn't pull through until Charon and John clear out the first wave of attackers,alongside Zero.