Beautiful tune and beautifully played by Ungar. As to whether it is “Classical” or not, while I’m not sure where exactly the genre dividing line can be drawn, it should be remembered that quite a few Classical composers have incorporated the folk music of their native lands in their works. Antonio Dvorak, Bela Bartok, Zoltan Kodaly, Manuel DeFalla, Ralph Vaughn Williams and in the USA, Aaron Copland of course, to name a few.
As to Ashokan, I know the area well. Beautiful area in upstate NY. Every time I drive by I marvel at how the water that comes out of my tap in NYC comes from a reservoir 130 miles away.