The reason for this in southern Austria/Burgenland is due to traditions surrounding inheritance, and is not related to farming methods. Landowners would divide their farm equally among their children rather than giving it to their oldest child. After many generations, the farms were carved down into the narrow strips you can see even today.
While farming methods didn't lead to the shape of the fields, the shape of the fields has determined what farming methods can be used today. They are impractical for large, modern farm machinery and in fact there has been consolidation of those fields in modern time so machinery can be used. If you look, you'll find discussions lamenting the change.
ETA: This map shows clearly remnants of the old style fields (the narrow strips) and larger plots that have been consolidated in Burgenland. And this map is another area where the old style fields largely remain.