I shouldn't have been so quick to doubt @rhickok1109!
I think the Yankees PR was just flipping the offensive position to defense. I found a program online mentioning the "defensive-quarterback". So the "defensive-center" in '49 would have been a linebacker like Ralph said. I don't think this use of terminology necessarily reveals anything about the defense they were playing though. My experience has been early media (programs, etc.) tend to be generic. Lots of programs don't list starters, just a roster. Often a position is just listed as "B" not distinguishing even between HB and QB, etc.
@rhickok1109, here's a question for you - where did the "defensive-quarterback" play if the offense was single-wing? It would be the tailback they would put at safety, right? I think I know the answer, just seems odd to imagine the player leading the way on a run as a blocker to also be a player who played outside like a modern CB on defense.