Concept for a Magic Melee DPS

[Archwizard]

Wouldn't beastmaster be considered magical? Maybe I should have elaborated a little more.

I guess it could be physical.

From the wiki,

The Beastmaster (魔獣使い, Majūtsukai?, lit. Monster Tamer), also known as Trainer or Mediator, is a job class that appears in various titles in the series. Beastmasters are characterized by wearing clothing similar to one who works with animals. Beastmasters have been known to use weapons from daggers to axes to whips. Their stats are usually physical in nature and their abilities include the ability to catch monsters and release them on their opponents, and can also Control the actions of opponents and lure them away.

The only magical aspects of the job are occasionally the methods they use to subdue monsters, and the magical abilities of monsters they control, of which the same monsters will often inflict physical damage as well or instead.
(Bearing in mind that NIN also uses magic damage in their techniques, and BLU also uses some physical techniques. In either case they are not known to cross-over into magical or physical DPS, respectively.)
Otherwise they don't have any kind of magical focus, and as their unique weapon is a whip in addition to the ability to command pets from a distance, it makes sense they would be more of a ranged job.