Interesting question ...!
I think the whole 'fine art photography' genre is open to interpretation, so I can't give a definitive answer to it but i have my own personal thoughts.
I think fine art photography is the high end of the creative craft. It's primarily non digital or at least has some connection with traditional photo skills - such as film, darkroom or alternative processes. Prints such as silver gelatine or especially platinum prints are also extremely archival and the latter last as long as the paper they are printed on - maybe 1000 years.
To me, digital photography is too easy, too clinical and somehow along the way digital photography loses it's soul. You really can't beat the tactile experience of developing a black and white negative in proper darkroom chemicals and watching the magic happen. It's almost like alchemy.
With all that said, I know art photographers who use digital cameras as a capture medium and then tweak the images to produce high end fine art too. A well done Giglee print on art paper also has an incredible tactile quality and the prints apparently last longer than traditional darkroom silver halide based materials.
Perhaps there is no definitive answer ... Some people might argue that Damien Hirst's sheep in formaldehyde isn't really art ... but somebody paid a lot of money for it so maybe it is !