A fatalist is a person who is extremely pessimistic. They are sure that bad things are going to happen to them and that there is nothing they can do to prevent those bad things from happening.
Winston is definitely a fatalist. The moment he writes "Down with Big Brother" in his diary, he knows that he is dead. This kind of an attitude, in my opinion, does help lead to his demise.
Because he thinks he's sure to get caught anyway, Winston takes some stupid chances. He rents the room over the shop, he goes to O'Brien's house for the "meeting" of the Brotherhood. He is not as careful as he ought to be.
If you feel like you're going to get caught and killed no matter what, why bother trying hard to avoid getting caught? That's what happens with Winston, I think.
According to the University of Stanford, fatalism refers to an "attitude of resignation in the face of some future event or events which are thought to be inevitable." (See the first reference link). In other words, fatalism is the idea that failure is guaranteed and we see lots of examples of this attitude in Winston's character. When Winston starts keeping a diary, for instance, being found out by the Party is all that he can think about:
theyll shoot me i don’t care theyll shoot me in the back of the neck i dont care down with big brother they always shoot you in the back of the neck i dont care down with big brother.
Winston is a fatalist because he understands the true power of the Party. From the telescreens to the memory holes, Winston knows that the Party is everywhere and, therefore, it is impossible to hide one's rebellion forever, as he comments:
He was already dead, he reflected…Now he had recognised himself as a dead man it became important to stay alive as long as possible.
As such, because Winston knows that the Party will catch him, he snatches at every opportunity to rebel. He buys and writes in his diary, for example, he develops a sexual relationship with Julia and he goes to O'Brien's apartment where he agrees to become a member of the Brotherhood. All of these actions are punishable by death but Winston does not care because he believes that his fate is already sealed. It is ironic, then, that Winston does not die at the hands of the Party but instead learns to love Big Brother.