StabiliTrak is a response to the car being yawed (it is pointing a different direction than it is actually moving). That system has a variety of tools to bring a car back into control.
Engine power is related to traction control and looks for wheel spin which is distinct from yaw. Here, the system will reduce engine power and/or apply brakes to limit the spin. This is what handles launch control.
Wheel spin can induce yaw via on-throttle oversteer, so the StabiliTrak system will limit engine power to fight yaw-inducement. The less restrictive a setting you use, the more yaw is allowed (therefore less engine power is withheld). A wet track is more traction-limited than a dry track, hence the wet setting is more restrictive than the dry setting.
My understanding is Competitive Driving Mode is that it uses the traction control system to manage the initial launch, but afterwards it does not further prevent wheel spin, and the stability control systems allow more yaw, and so its possible to spin the car (say, by off-throttle oversteer). Other settings stay as they were.
