Adding the signal (input) in the way you did is absolutely the same as setting a setpoint. The same.

I don't think it is the same.

there is no need to MULTIPLY THE GAIN WITH THE SETPOINT ( set point is already in error value which is the difference between the gyro and the set point )

This is only true when your setpoint (as determined by your control input) is zero.

Normal PID:

output = Pgain *(actual - setpoint) + Igain*(sum of errors) + Dgain*(change in error)

Your controller:

output = Pgain *(actual) - setpoint + Igain*(sum of actual) + Dgain*(change in actual)

(here 'actual' will be your gyro reading)

(I believe normally it would be written as setpoint-actual but it doesn't matter too much)

Ignore I and D for now, and consider the following scenarios:

A) Pgain = 2, actual = 10, setpoint = 0

normal PID output = 2 * (10 - 0) = 20

your controller output = (2 * 10) - 0 = 20

Now the setpoint is not zero

B) Pgain = 2, actual = 0, setpoint = 30

normal PID output = 2 * (0 - 30) = -60

your controller output = (2 * 0) - 30 = -30

C) Pgain = 2, actual = 0, setpoint = 50

normal PID output = 2 * (0 - 50) = -100

your controller output = (2 * 0) - 30 = -30

I hope you can see that your controller is unaffected by the Pgain and therefore the response

is not proportional to the error (difference between setpoint and actual) which is the point of a P controller.

Now see this scenario:

D) Pgain = 2, actual = 20, setpoint = 20

normal PID output = 2 * (20 - 20) = 0

your controller output = (2 * 20) - 20 = 20

In this case you are exactly where you want to be, so there should be no output, but your controller is still trying to correct the motors!

(If Pgain = 1 then you won't see this)

Now consider the I term:

E) actual = 20, setpoint = 20

normal PID error to add to I term: 0

your controller error to add to I term: 20

The error will be zero, but your Iterm will keep growing and affecting the output when you don't want it to.

What you are doing does not make sense. The issues with it are somewhat masked (I assume) by having a Pgain of 1, and mostly wanting a setpoint of zero.