Both empire and an empire are grammatically correct. Omitting the article treats the concept in a dreamy, hazy, abstract way. It suggests that the Nazis' goals were grandiose and poorly thought through, which agrees with the claim later in the sentence that the Germans went about it all wrong. Including the article would treat the Nazis' goal of making an empire prosaically, simply as their goal, without the connotation of haziness or grandiosity.
Omitting the article in the sentence you quoted echoes some other dreamy, hazy uses of nouns. In these examples, including an article would not be grammatically correct, because each noun in boldface is a "mass noun":
Thousands of girls moved to Hollywood seeking stardom.
And who shall blame the poor for dreaming of wealth? [Source]
The word empire is not normally a mass noun. Empires are distinct, countable things. They're not vague qualities like stardom or wealth. So, treating empire as a mass noun is unusual. It suggests thinking of "empire" in an out-of-focus, hazy way, just as the people described above think of stardom and wealth. That's why it's so appropriate for the sentence you quoted.
Here is a famous quotation where some nouns that can be count nouns are treated as mass nouns in order to make the reader think of them as abstract qualities rather than specific things:
"Nothing in this world can take the place of persistence. Talent will not; nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not; the world is full of educated derelicts. Persistence and determination are omnipotent. The slogan 'press on' has solved and always will solve the problems of the human race." [Attributed to Calvin Coolidge]
The author could have said a talent or talents or an education, but that wouldn't have the abstract quality the author was trying to convey.