Interesting: Notice how aux in this sentence is translated as "nor" in English. How would you say: "I do not like either coffee or wine" (it's obvious that there are very little real situations where you'd have to say that exact sentence, but you get the idea).
I believe "ol" is a conjunction. This sentence is short for "Mi ŝatas kafon pli, ol mi ŝatas vinon." as in "I like coffee more than I like wine". The accusative comes from the word's role in the second clause that doesn't generally get spoken.