I might have mangled my explanation of this! Their analysis wasn't merely of "what word is most common in Macbeth", or even, "what word is most common in all of Shakespeare's plays". In that case, yes, the obvious winner would have been "the", since it's the most common word in English overall.

But their analysis was probing a different question, which was: "In Macbeth, what are the words Shakespeare uses *far more frequently than he does in his other plays*?"

So obviously words like "thane" would pop out, because Shakespeare really never used those in his other plays.

But the word "the" also popped out. He used it far more frequently than he used it in his other plays. Or to put it in numerical terms, if he used "the" in Macbeth at the same frequency he used it in his other plays, there would be 150 fewer "the"s in Macbeth. He used it 150 more times than normal.

That's what made it interesting, and significant!