Okay.
I am of the mind the book is very dry, a tad bit dull and too preachy. For that reason above all else I tend to think the best interpretation was James Whale's two movies (he only did TWO the crap sequels were not his making) in Frankenstein (1931) and Bride of Frankenstein (1935)....
With that said I would argue that Branaugh's film was actually quite accurate towards the book in the sense of plotting. With the exception of Elizabeth being brought back from the dead, the storyline was very faithful as was character interpretations (save for the modernizing of Elizabeth, but hey for someone "so important" to the novel, she had no depth or development or arc whatsoever, like every other supporting part in the novel.....that's going back to my first point)...
Now whether it is a good film or not is a different story. Quite frankly I think it is melodramatic, too over the top and knows not the meaning of the word subtelty. There are certain scenes that are still very stirring, such as any scene Robert DeNiro is onscreen. The man can play ANYTHING. He is not Boris Karloff, but quite frankly his is probably closer to what Shelly wrote, again go back to my point about preferring Whales' films though.
Anyway, he is great, the cinematgoraphy beautiful and certain scenes iconic, even if the plot point is wretched (I loved the red cloak climbing the staircase as he goes to raise Elizabeth back from the dead, though I thought the whole tangent was pointless and disgusting). I also think Patrick Doyle wrote some of the most gorgeous and haunting music ever written for cinema for this film.
But the overall direction is mediocre, despite good performances all around (save for Branagh himself who works well in his early Shakespere adaptations but between this and his rather Erroyl Flynn-droole Hamlet, hbe peetered out).
Oh...as for the question at hand
No it is not a Greek tragedy, for it is not a play written in the era between 323 B.C. to the birth of Christ.
But hey, it does have themes of Greek tragedy. Frankenstein was obviously all huburis and had to learn the costly lesson and the monster's tale is a sad one that is tragic. What he does to Elizabeth is evil but after the cottage scene and him crying over his father's body on the boat and death....he is still endearing. This movie would be unwatchable if not for the charismatic Robert DeNiro in my opinion. And yes, the characters all exude the bare simplistic traits of Greek tragedy.
But if you REALLY want to make a horror tale into a Greek tragedy, than The Wolfman would be the way to go then.