Oxidizing means to combine with oxygen. Sounds harmless right? When molecules combine with oxygen, negatively charged electrons are released, and this causes things to break apart. So when an oxidizing chemical such as bleach or hydrogen peroxide comes in contact with a pathogen, it literally rips it apart.
Non-oxidizing chemicals such as alcohol or Quaternary Ammonia are compounds that tend to hold a positive electrical charge, making them able to stick onto cells (bacteria cell walls tend to be negatively charged). This sticking action causes cells to coagulate or clump together. Think of them as making things sticky, but on a microscopic level.