Impossible Architecture

In general the main solution is teleporting as you already mentioned. Visual portals are not necessarily required if you have a clever map design. However in certain situations you just don't have enough room to only use map design as you would have to duplicate large portions of the map or you can't have the transition points too close together.

So your first example video would be hard / almost impossible without visual portals.

The second one (from what we have seen) would be possible just by level design + teleport. Though since it's made with source they might also simply use portals.

Ok so I have made myself a little game where you can wander around and in one direction there is an endless hallway, in the other is a "bigger on the inside" corridor. I didn't use any portals for the hallway, a simple teleport was far easier. However for the corridor of course a teleport was necessary. Works ok but is quite obvious there is a plane there.

Firstly there's a slight white tint to it. not sure where it's coming from but it looks like you're looking through a window.

Secondly, when facing one direction the camera rotation seems to be a frame out and so you see outside the hallway. I have no idea why this is happening though.

Here is a video demonstrating what I have so far and the issues with it

The lag on the other cameras is the biggest issue, how can I stop that? Induced all my code for reference.

 using System;
 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 using UnityEngine.SceneManagement;
 
 public class portal : MonoBehaviour {
 
     public RenderTexture rt;
     public GameObject thisPortal;
     public GameObject otherPortal;
     public Shader cropShader;
     public Boolean inPortal;
     public float distance;
     public float clipping;
 
     private GameObject thisPlane;
     private GameObject otherPlane;
     private GameObject player;
     private Material mat;
 
     // Use this for initialization
     void Start () {
         thisPortal = this.gameObject;
         thisPlane = thisPortal.transform.GetChild(0).gameObject;
         otherPlane = otherPortal.transform.GetChild(0).gameObject;
         player = Camera.main.transform.parent.gameObject;
         rt = new RenderTexture(Screen.width, Screen.height, 16, RenderTextureFormat.ARGB32);
     }
 
     // Update is called once per frame
     void Update () {
         MoveCamera();
         Clip();
         if (IsOnScreen(thisPlane))
         {
             //Debug.Log("is on screen");
             CreateRenderTexture();
             
         }
         else
         {
             //Debug.Log("is not on screen");
 
             DestroyRenderTexture();
         }
 
         if (Input.GetKeyDown("r"))
             SceneManager.LoadScene(0);
     }
 
 
     // When you look at the portal, switch on the camera and create the renderTexture
     private void CreateRenderTexture()
     {
 
         if (rt.IsCreated() == false)
         {
             //Debug.Log("Render texture doesn't exist... Creating");
             rt.Create();
             transform.GetChild(1).gameObject.GetComponent<Camera>().targetTexture = rt;
             transform.GetChild(1).gameObject.GetComponent<Camera>().enabled = true;
 
             mat = new Material(cropShader);
             mat.mainTexture = rt;
             thisPlane.GetComponent<MeshRenderer>().material = mat;
         }
     }
 
     // When you are not looking at the portal, delete the texture and turn off the camera to save resources
     private void DestroyRenderTexture()
     {
 
         if (rt.IsCreated())
         {
             //Debug.Log("Render texture exists... Releasing");
             rt.Release();
             transform.GetChild(1).gameObject.GetComponent<Camera>().enabled = false;
             transform.GetChild(1).gameObject.GetComponent<Camera>().targetTexture = null;
             thisPlane.GetComponent<MeshRenderer>().material = null;
             
         }
     }
 
     // Moves the exit portals camera so it matches the mainCamera's relative position and rotation to the entry portal
     private void MoveCamera()
     {
         var portalPos = thisPlane.transform.position;
         var otherPortalPos = otherPlane.transform.position;
         var mainCamPos = Camera.main.transform.position;
 
         var playerOffset = mainCamPos - otherPortalPos;
         otherPortal.transform.GetChild(1).position = portalPos + playerOffset;
 
         otherPortal.transform.GetChild(1).rotation = Camera.main.transform.rotation;
     }
 
     // Checks if any point of an object is on screen
     private bool IsOnScreen(GameObject obj)
     {
         // Defining top left, top right, bottom left, bottom right and middle
         Vector3 TL;
         Vector3 TR;
         Vector3 BL;
         Vector3 BR;
         Vector3 mid;
 
         // Assigning each of the above a point in world space based off the objects bounding box
         BL = Camera.main.WorldToScreenPoint(obj.GetComponent<BoxCollider>().bounds.min);
         TR = Camera.main.WorldToScreenPoint(obj.GetComponent<BoxCollider>().bounds.max);
         BR = Camera.main.WorldToScreenPoint(new Vector3(obj.GetComponent<BoxCollider>().bounds.max.x, obj.GetComponent<BoxCollider>().bounds.min.y, obj.GetComponent<BoxCollider>().bounds.max.z));
         TL = Camera.main.WorldToScreenPoint(new Vector3(obj.GetComponent<BoxCollider>().bounds.min.x, obj.GetComponent<BoxCollider>().bounds.max.y, obj.GetComponent<BoxCollider>().bounds.min.z));
         mid = Camera.main.WorldToScreenPoint(obj.GetComponent<BoxCollider>().bounds.center);
 
         // Checking if any of these points are on the screen
         if (IsBetween(BL) || IsBetween(TR) || IsBetween(BR) || IsBetween(TL) || IsBetween(mid))
         {
             return true;
         }
 
         // There is a possibility that the player is standing so close to the wall that all the points are outside their cone of vision, so we check if they are within 3 units of the portal
         else if (Vector3.Distance(transform.position, Camera.main.transform.position) < 10)
         {
             return true;
         }
 
         else
         {
             return false;
         }
     }
 
     // This method just neatens up the IsOnScreen method by doing all the repetative working
     private bool IsBetween(Vector3 v3)
     {
         // Defining the min and max width and height with a 1/3 buffer so you don't catch an untextured plane when you turn too fast
         var minWidth = 0 - Screen.width * 0.3;
         var minHeight = 0 - Screen.height * 0.3;
         var maxWidth = Screen.width + Screen.width * 0.3;
         var maxHeight = Screen.height + Screen.height * 0.3;
 
         if (v3.x > minWidth && v3.x < maxWidth && v3.y > minHeight && v3.y < maxHeight && v3.z > 0)
         {
             return true;
         }
         else
         {
             return false;
         }
     }
 
     private void Clip()
     {
         var cam = transform.GetChild(1).gameObject;
         var dist = Vector3.Distance(transform.position, Camera.main.transform.position);
         
         if(dist >= 9)
         {
             cam.GetComponent<Camera>().nearClipPlane = dist - 5.8f;
         }
         else if (dist < 9 && dist > 3)
         {
             cam.GetComponent<Camera>().nearClipPlane = dist * 0.75f;
         }
         else
         {
             cam.GetComponent<Camera>().nearClipPlane = dist * 0.5f;
         }
         distance = dist;
         
     }
 
     private void OnTriggerEnter(Collider other)
     {
         Debug.Log("in");
         if (inPortal == false)
         {
             inPortal = true;
             otherPortal.GetComponent<portal>().inPortal = true;
             player.transform.position = otherPortal.transform.position - (thisPortal.transform.position - player.transform.position);
         }
     }
 
     private void OnTriggerExit(Collider other)
     {
         Debug.Log("out");
 
         StopCoroutine("Wait");    // Interrupt in case it's running
         StartCoroutine("Wait");
         
     }
 
     IEnumerator Wait()
     {
         yield return new WaitForSeconds(1);
         inPortal = false;
         otherPortal.GetComponent<portal>().inPortal = false;
     }
 }