What role does fatalism play in the plot ?

There is very little fatalism or "classical" fate or determinism in Macbeth.  The role of "time" determines the plot, not "fate."  "Murder" determines the plot, not "fate."  "Evil" determines the plot, not "fate."  The Macbeths determine the plot, not "fate."  Whereas Oedipus was dealt a heavy does of fate, Macbeth chooses to murder, to be evil, to defy time.  He is an agent of free will, not a victim of prophecy.

The witches may seem to be instruments of fate or fatalism, but they are preachers to his choir: they tell him what he wants to hear.  They are like the chorus--in the play, but not in the play.  The witches simply supply Macbeth with the nouns (Thane of Glamis, Thane of Cawdor, King Hereafter).  They are not like the Oracle at Delphi, which supplies the verbs (you will "kill") and the direct objects (your "father").  Lady Macbeth supplies Macbeth with the verb of "murder" and the direct object "Duncan."  No one claims that she is an instrument of fate, so why then the witches?

And, other than the "hereafter" adverb, the Witches do not specify a time frame.  Macbeth might have waited until he was an old man to become king.  Macbeth actively speeds up time in the play: his "vaulting ambition," his "deep desires," his id cause time to spin out-of-control, against him.  Driver says there are three kinds of time in the play:

(1) time measured by clock, calendar, and the movement of sun, moon, and stars, which for the sake of convenience we may call "chronological time;" (2) an order of time which overarches the action of the entire play and which may be called "providential time;" and (3) a time scheme, or an understanding of time, belonging to Macbeth, which maybe called "Macbeth's time." (Driver 143-44)

If the tragic hero has his own time, how can he be a victim of fate?  Time and fate only appear to be linked.  Macbeth tries to control or defy time, but he cannot.  He stopped Duncan's tomorrows, and he tries to stop his own.  Inevitably, tomorrow catches up to him.  "Tomorrow" is the key word in Macbeth that refutes fatalism.  Macbeth's famous soliloquy is prime example, but there are others in Acts I and II of equal importance; so says Driver:

In one instance, it appears that Macbeth escapes his prison of destiny. When questioned by his wife about the time of Duncan’s departure, Macbeth replies, “Tomorrow, as he purposes” (1.5.60). Lady Macbeth, now obsessed with her disgusting plan, insists that “never shall that morrow see” (1.5.61). They succeed in making sure that Duncan never sees another light of day, but their disturbance of nature does not change fate in their favor. Instead, they have caused chaos in Scottland, and what should be light and good is now dark and evil.

Key phrase: "they have caused chaos"  Notice, it is not "chaos has caused them."