Translation:He boxes while dreaming of classical dance.
I believe 'de la' would be the 'partitive', which is used when talking about some unspecified quantity. But here 'dance' is not a quantity - there can't be dreams of some portion of dancing. In addition the definite pronoun 'le' would not make sense either, as it's not referring to some specific instance of dancing, but rather dance in general.
I guess part of the confusion is why the boxing part of the sentence is different, and does include the partitve, being translated as "fait de la boxe". After a quick Google search, it looks like the 'de la' (or 'du' for masculine) always follows the conjugation of 'faire' in phrases like this.
Perhaps there is some good explanation, but you may just have to think of it as a fixed phrase/construction that has to be memorized.