How to implement Google Map App style gesture in Unity?

For all methods, you'll need to store/access the old touchpositions from the previous frame. Also, raycast into the scene through (touchpoint1.screenposition+touchpoint2.screenposition)/2 to find your center of reference.

Scale (implemented as a translation of your camera's position towards/away from the center of reference):

• Compute the difference of Distance(touchpoint1.screenposition,touchpoint2.screenposition) and Distance(oldtouchpoint1.screenposition,oldtouchpoint2.screenposition) to find out how much you want to zoom in/out. The resulting zoom seems more intuitive if you use the difference, as opposed to the quotient.

• Compute the direction cam2reference=centerOfReference-camera.transform.position;

• Add cam2reference*touchdifference*scaleSpeedFactor*Time.deltaTime to your camera's position each frame

Rotation (implemented as a rotation of your camera around the center of reference):

• Compute the angular difference between the two old and new touch points (see below)

• Use camera.RotateAround(centerOfReference,Vector3.up,angularDiff*rotateSpeedFactor*Time.deltaTime) each frame

Some example code that works for me (although it might be possible to make this simpler using some of the convenience functions Unity provides):

 // get angular difference
 float angleNow = Mathf.Atan2(touchpoint1.screenPosition.y - touchpoint2.screenPosition.y, touchpoint1.screenPosition.x - touchpoint2.screenPosition.x) * Mathf.Rad2Deg;
 float angleThen = Mathf.Atan2(oldtouchpoint1.y - oldtouchpoint2.y, oldtouchpoint1.x - oldtouchpoint2.x) * Mathf.Rad2Deg;
 // wraparound failsafes (wraparound of Mathf.Atan2 is at +-180)
 if(angleNow>90&&angleThen<-90)
     angleNow-=360;
 if(angleNow<-90&&angleThen>90)
     angleNow+=360;
 angularDiff = angleNow - angleThen;