IMO, the gist of this signing is most likely replacing Vanek's role as a middle-6 stop gap mentor/leader with a guy that can do all of the same things, but also kill penalties, take some faceoffs and actually play in his own zone.
While the Red Wings have a lot of center depth, Larkin and Nielsen were the only ones that can provide some offensive acumen while also being able to fulfill all the duties of a player at that position:
Larkin - Good #1C/PK/PP
Nielsen - Good #3C/OK #2C/PK/PP
AA - Can play C, but probably better suited at wing
Glendening - Solid #4C/Can fill in at #3C, but not ideal/PK
De La Rose - Good #4/5C, didn't look great when moved up the line-up and on the PP, might be better suited at wing
Ehn - Good #4/5C with upside, but probably needs more time as a top center in the AHL, or on the wing in the NHL
Helm - Can fill in as a bottom 6 center, but really hasn't played the position much in the past 6 seasons...
Abdelkader - Can fill in as a bottom 6 center, but really hasn't played the position much at all in the past 6 seasons...
Rasmussen - Not ready to take on a regular role as a C in the NHL, needs to either play the position in the AHL, or more time at wing in the NHL
Turgeon - Likely a Cory Emmerton 2.0 passable #4/5C fringe NHL guy
Veleno - Probably needs a full season in the AHL before he's considered for a spot in the NHL
Yzerman has already come out and said AA will play wing, so they needed somebody to fill the gap between Nielsen and Glendening, and be able to move up to a #2C spot and center a PP if Nielsen or Larkin get hurt.
Filppula and Nielsen will probably get juggled around as 2C and 3C and centering the PP when Larkin isn't out there.
Maybe they'll also alternate wearing #51?