Are aircraft engines classified as DAL A or DAL B?
DAL started in the software world with DO-178, but it has been extended to the entire development process.  This is documented in ARP4754A Guidelines For Development Of Civil Aircraft and Systems and ARP4761 Guidelines and Methods for Conducting the Safety Assessment Process on Civil Airborne Systems and Equipment.  

But to the direct question, 14 CFR 33.75 Safety Analysis, describes the safety levels required for the engine.  Matching the wording there  


  (3) The applicant must show that hazardous engine effects are
  predicted to occur at a rate not in excess of that defined as
  extremely remote (probability range of 10−7 to 10−9 per engine flight
  hour).


with ARP4761, it is describing DAL B.  So I would have to agree with the speaker.  

But I will offer one point of personal experience which is that one FAA certification officer insisted the DAL for the FADEC software should be DAL A.  The argument is that a common mode fault in the FADEC software could result in simultaneous loss of both engines.  

One other fine point of certification is that complying with Part 33 allows you to get a Type Certificate for the engine.  That doesn't mean it meets all the requirements necessary to allow an aircraft with that engine installed receive an aircraft Type Certificate (under Parts 23 or 25).