I have almost the exact same question as the OP. I am about to start a hat pattern that calls for a left twist and I have seen two different versions on Youtube, just like the OP.
The instructions for the hat say:
Left Twist - Slip the next 2 stitches knitwise (separately, not together). Place both stitches back on the left needle as they are (twisted). Knit second stitch through the back loop, keeping the stitch on the left needle, then knit both stitches through the back loop, dropping both stitches from the needle.
My question is, do I really need to slip the stitches and then knit the second stitch through the back loop and then knit both through the back loop or can I just skip the "slip" part? None of the videos I have seen on left twist involve slipping stitches. Since it is written in the pattern to do it this way, I most likely will follow but I really would like to save myself any unneccesary maneuvering. The more manipulating of stitches I have to do, the more likely I will make a mistake and then be unable to rectify it later.