Nope, look at the wording. It adds your INT bonus as a modifier to all STR and DEX checks, without mentioning that you lose the STR or DEX bonus. As an aside, it's one way for certain high-level arena builds to get some absurd initiative bonuses, among other things - a Sorcerer/Swiftblade gestalted with Factotum/Marshal+Motivate Dexterity is adding DEX once, INT once, and CHA (casting stat) twice to their initiative modifier.