In his pre draft press conference he said "trust your board, build it for your team. We don't grade for the league we grade for the Buffalo Bills, how we value players, how we use players and that's how you get some differences on where players are graded." Beane puts an emphasis on "Bills DNA" and specific traits at positions of need. About the pick he said he wanted to add speed to the room at a position of need.
Personally that wouldn't be anything I consider at all when taking your first pick. You take the best football player on the board which is what the Eagles do which is why every year everyone is like omg how did they get that guy? Because guys fall for whatever reason, GM's being cute drafting for need over talent, and then the Eagles just take the best guy on the board. There's no trick to it. I think GM's are outsmarting themselves when sometimes the simplest solution is the best one.
Later on in the draft it's a real concern that the guy can even make the team. That's when then it's ok to draft for specific needs and traits. You want the guy to have a chance to make the team. That's not a problem at the top of the draft. I think the Bills have had lackluster results in rounds 1-2 and they need to do something different (I prefer the Philly model). Later rounds I fully trust they will do what's best for the team.