Can you analyze this Cinematic end-game? 'The Luzhin Defense'

I remember watching this movie while on a trans-atlantic flight.  John Turturro is one of my favorite actors and I will pretty much watch anything he's in without question.

 

The movie 'The Luzhin Defense' didn't really make a lot of headway in the US, but I really enjoyed the movie.  The movie was based off of a novel by Nabakov (Lolita) about his close friend, Curt von Bardeleben, who committed suicide in 1924.

 

Here is a diagram for the final moves of the game between Luzhin (Turturro) and his arch-rival, Turati.  Luzhin is black and is behind on material.

 

As we havel often seen in sports or competetive events depicted in cinema, at times; the actual moves can be very elementary.  I'm interested in hearing an analysis of this end-game from our fellow chess.com community members. 

 

The film is gripping and fitting of most Turturro roles.  I highly recommend it. 

It first looked drawn to me.  1.Kg4 f5+ (1...h5+ 2.Kg5 Kg7 3.Nd5 draws) 2.Kg5 Kg7, threatening 3...Be7 mate.  But after 3.Nd5 Rh3!! (3...h6+ 4.Kh4) 4.gxh3 h6+ 5.Kh4 Bf2 mate since White can no longer go to h3.  But White can avoid mate in 5 with 1.Kf2.  But after 1...Rxc3 2.Kd2 Rxc1, the game is over, it just takes longer to mate.  Now, who was the composer of this problem?  Jonathan Speelman was the chess advisor for the film.  Did he create this problem himself, get it from somewhere else, or is it a creation of Nabokov, who was known as a chess problemist.  By the way, the movie credits list the chess advisor as John Speelman, not Jon Speelman.

I only watched the trailer of the movie and they explained a bit what was the scenario in it, and basically it looked SOOOO different from the book (excellent book, by the way), from the plot to the characters (Luzhin in the book is quite the opposite as in the movie)... And they made the movie much less psychological and more "political". I'll probably watch it sometimes, but I don't really like watching television...

 

" It looks drawn to me.  1.Kg4 and 1...f5+ or 1...h5+ 2.Kg5"

But if you follow the moves, you see that it loses. 

Could you please help show how? Black has a lull that white could use, perhaps

Either 3.Nd5... or 3.g4....

Just play the move on the diagram haha. I'll give you the moves as perhaps it doesn't work on your computer? After 3.Nd5 (trying to prevent Be7++) 3. ...Rh3 4. gxh3 (or h6++) Be3++

 

as for 3.g4? Be7++ 

brilliant!