Is the zombie lord a zombie?
No, the Zombie Lord is not a zombie.

As you said, logically he wouldn't be a zombie, because if he was they would just say kill the zombie lord for the requirements for winning the game (page 25)

Additionally, the rules for that haunt remind you that the Holy Symbol that affects all Zombies, doesn't affect the Zombie Lord:


  If you have the Holy Symbol, all Zombies who make Might attacks against you roll two fewer dice. (This doesn't affect the Zombie Lord.)


It hasn't been confusion for many other players, so no additional information appears in the FAQ, or on BGG regarding the Zombie Lord.