The term "back then" is referring to a time in the past. The word "then" is used to relate to time whereas the word "than" is used in comparisons. For this instance, you would use "then". The author could use "The same as I did back then" and "The same as I did then"...they would both make sense and mean the same thing. The omission of "I feel" is probably an artistic choice for the author. You are right that the proper sentence would have "I feel" in it but many authors of english will sometimes use incomplete sentences to make the story sound more like spoken english or for dramatic feel.