Two years ago today, the guns were supposed to fall silent. They
This means that on the same day and month as today, but two years ago, the guns were supposed to fall silent.
"They didn't" implies that the expected event (of guns falling silence) did not happen back then. Maybe it happened some time later, but that information is not included and we do not also know the present status of the argument.
Two years ago, Russian fighters were supposed to begin leaving eastern
Ukraine. They haven't.
This means that two years ago something was supposed to happen.
"They haven't" implies that to this date, the event has not happened. Notice that
"they haven't" is in the present tense and it communicates the present status of the event.