Only the Chrome extension of Privacy Badger uses ABP code. And it only uses it for managing the blocklists it creates. Most of the function of Privacy Badger is run separately from the ABP code, and to be honest my first task for the next version is to get rid of ABP completely :)
Privacy Badger currently detects tracking via regular cookies, HTML5 local storage 'cookies', and canvas fingerprinting, with more methods aimed to be supported in future releases