My bad. It seems the sword is primary and not secondary weapon. Anyway this puts the Kuarothoroi on par with Macedonian and Seleukid Hypaspistai. Basically a heavy phalangite that can fight extremely well in a melee. Just remember to use the sword against infantry and the spear against cavalry.
I see no anti cavalry bonus in the EDU no mount_effect, spear_bonus, spear or light_spear. This unit has no bonuses against cavalry.