the stock shifter may slow your shifts a little and may make it harder to find the gear you want but you can still chirp the 1-2 and 2-3 shifts. I have done both and I let off the gas between shifts
hmmm....how to explain
In normal driving, you push the clutch in while letting off the gas and moving the gear selector and then let out on the clutch while stepping back on the gas.
You are trying to accelerate as fast as you can when you do the tire chirp thing. Shifting is the same as normal, only you are shifting as fast as you can; the rpm's will still drop between shifts, only you are letting out the clutch so fast (they call it "dumping the clutch") and giving it gas so fast that by the time the clutch comes out all the way, you have applied enough power with the gas pedal that the car can't quite accelerate as fast as your drivetrain wants to push it, the tires break traction for a moment and you get a chirp...
you do not have to stomp the gas all the way to the floor to do this, and you want to be careful because you are flirting with the edge of vehicle control. Just because you chirp the tires does not mean you are accelerating as fast as the car can, it takes practice and finesse to be quick. Practice hard accelerations and get used to the power and you will see. Just like it takes practice and finesse to drive the car normally with smooth shifts. It may have taken me 10000 miles but now I can shift smoothly enough not to feel a thing
Yes, this kind of 'spirited driving' does cause wear and tear on the equipment and you don't want to do it all the time