At least as I would perceive it organizationally a GM functioning under a President of Baseball Ops would function for the world of professional players (trade candidates) as the Director of Player Personnel would act for the organization's minor league players and the pool of amateur and international players. The GM would also be responsible for rolling all of that data up into an organized portfolio of potential call ups, draft and trade candidates for the Pres of Baseball Ops. GM probably handles the administration paperwork of trades and contracts as well.
Remember, while we tend to think of the Pres of Baseball Ops as totally about players, there is the rest of the front office for the President of Baseball Ops to handle, the analytics dept, all of the coaches, major league and minor league, it all falls into his lap.
Now that Kennedy is the CEO of the Red Sox, DD and any other Pres of Baseball Ops would report through Kennedy with Kennedy now having all the business end responsibilities just as he had as President of the Team now including acting as the reporting channel for the President of Baseball Ops up to ownership.
I don't have a Sox org chart but having been an exec in a business, looking at the position titles and general responsibilities that is how I would suggest they are organized with the GM functioning in the role I suggest.