Indeed, 'entire scene' refers to the world position.
The THREE.Vector3() object includes an applyMatrix4() method,
You can achieve similar results as the shader by projecting a vertex into world space using the following code:
yourPoint.applyMatrix4(yourObject.matrixWorld);
To convert this into camera space, you can use the next snippet:
yourPoint.applyMatrix4(camera.matrixWorld);
In order to obtain screen coordinates ranging from -1 to 1:
yourPoint.applyMatrix4(camera.projectionMatrix);
You can access your point like so:
var yourPoint = yourObject.geometry.vertices[0]; //first vertex
Instead of performing these operations separately, you can combine the matrices. While untested, the concept would be something like this:
var neededPVMmatrix = new THREE.Matrix4().multiplyMatrices(yourObject.matrixWorld, camera.matrixWorld);
neededPVMmatrix.multiplyMatrices(neededPVMmatrix, camera.projectionMatrix);
For a detailed explanation of what is happening behind the scenes, I recommend this tutorial.
Alteredq has provided comprehensive information about three.js matrices in this post.
Edit
If you only require the rotation without translation, you must utilize the upper 3x3 portion (rotation matrix) of the model's world matrix. This process may be slightly more complex. Consider using the normalMatrix or converting THREE.Vector3() to THREE.Vector4() and setting .w to 0 to prevent translation.
Edit2
In case you need to move the line point in your scenario, instead of applying it to the particle, apply it to
var yourVertexWorldPosition = new THREE.Vector3().clone(geo.vertices[1]); //this represents your second line point, whatever you defined in your init function
yourVertexWorldPosition.applyMatrix4();//this transforms the new vector into world space based on the matrix you provide (line.matrixWorld)