I would claim that it is highly unlikely that the description of the events are truthful.
According to an description of the meeting from the website of the President of Finland (which was Ahtisaari in 1999, when this meeting happened), there is at least one part of that description that was true: This was not a negotiation. The meeting was to present the NATO/Russian proposition. The negotiations were between NATO and Russia, and Ahtisaari was brought in as a third part in those negotiation as he had proven to be a good mediator earlier.
NATO explicitly did not want to negotiate with Milosevic.
But that's not of course what the text really is about. That Milosevic obviously didn't have a chance once NATO decided to stop the war was pretty obvious. He of course had no chance to win a war against NATO. This was probably obvious to him as well.
The purpose of the text is to claim that Ahtisaari (and therefore NATO) threatened to kill half a million Serbs if Milosevic didn't agree to the proposition.
The question then is if Ahtisaari really made those claims, and really made a sweeping gesture on the table, indicating that NATO would flatten Belgrade?
Of course, only the people in that room really knows, and at least two of them are already dead. But what is clear is that after that meeting, Milosevic needs to convince everyone else that agreeing to the proposition is the right thing to do, and since the proposition includes Serbian withdrawal from Kosovo, that will be a very hard pill to swallow.
Would that pill be easier to swallow if they had no option? Is it easier to accept if the alternative is half a million dead? Well, of course.
But would NATO really carpet bomb and flatten Belgrade? Of course not. They already knew from long before that bombing civilians isn't seen with kind eyes, and was in the bombing of Yugoslavia aiming at military and strategic targets, although of course there were civilian casualties. But a mass destruction of Belgrade would have not have been accepted by people, media or politicians in the west.
And I don't think Milosevic was stupid enough to believe it would be accepted. So I don't think Ahtisaari made any such threats, because it would have made him seem like a fool. It's most likely that this is Milosevic excuse for agreeing to a proposal he knew he didn't have much choice than to agree to.
The quotes about Ahtisaari making a sweeping gesture over a table comes from Ljubisa Ristic. Then a politician, now it seems like he is a movie director. I think we can ascribe the creative license to him. :-)