not trying to imagine up a brand new job but from what I've seen and read about red mage it is obvious they are mostly trying to just embrace the dps side of the job and the playstyle currently looks to be some hybridization of black mage/ninja and monk to a degree

my current vision of what they have given us so far will be it starts casting like a black mage, the spells likely "charge up" the sword rather than the astral/umbral cycle, once the sword is prepared you go in for melee combos which deplete the sword but charge up a chainspell buff, once the chainspell is prepared you cast it like mudras by picking the components and getting your combined chainspell. rinse and repeat

and it sounds like the healer aspect will be they get a spell like tetragramaton and a res(maybe even an ogc one?)
i'm betting their mp regen will be an additional effect on a sword skill and maybe have a backup whm shroud style one for recovering from mess ups

and then the standard suite of dps cooldowns that are all a little different to fit the flavor of the job while ultimately accomplishing the same thing