NINJA and ROGUE confirmed

[Reynhart]

A Rogue/Ninja/Thief/etc. has almost always (if not always) used dexterity and agility in their damage formulas.

Ok, people really need to stop using "always" when they say ONLY IN FFXI. Which is technically wrong too since STR and its effect on Attack had a far greater impact on calculating damage than DEX.
And in FFXI, AGI (Which our DEX is far closer to) was useful only for Trick attack, and ONE WS for Dagger or Katana.

And in EVERY offline game, Strength improved attack power, thus physical damage. http://finalfantasy.wikia.com/wiki/Strength