Assuming you knit right handed (from left needle to right needle). I do not know if I succeed in explaining this as I am not very good in explaining things in English.
If you have two stitches and you want to do a decrease, you need to imagine stacking them on top of each other and then pulling the yarn through both. Either the left stitch can be on top (k2tog) or the right stitch can be on top (ssk). The passo-decreases does the very same in two steps: first the working yarn is passed through the lower stitch, then by passing the other stitch over you take it through the upper. Anatomically, the very same thing happened as if you did k2tog or ssk. The only difference is in how tight you got the result.
Normally SSK is done by slipping both stitches knit-wise. The way you do it, by slipping the second purl-wise, you twist the lower stitch, which is tightening the decrease a bit. Basically SYTK is the more extreme of the same concept: the lower stitch is getting even more twisted.
(At this point, before doing more explanation I want to add one slight correction: when slipping the first stitch knit-wise in SSK you actually change the orientation of the stitch, so you do not knit through the back loop, as you wrote, but through the front loop. Normally the front loop is on the left side but with knit-wise slip it ends up on the right side.)
When knitting I have a bit of OCD: I want everything as perfect as possible. Thus I could not stand the thought of not making a perfect anatomical mirror of k2tog. Because of this I never do the twisted variants of SSK nor SYTK. Instead I have to do something else that can be use in many decreases. Now imagine you doing an SSK (with both slipped knit-wise). You have just pulled through the working yarn and you want to slip the stitches off the left needle. At this point you just slip off the top stitch but the other one you leave on the left needle and you yank with it so the top stitch will get tight. Now you slip it off and you open up the following stitch fully and it will pull the slack you created in the previous step. Basically you moved the slack from the loose SSK out of it.
This same idea could be used with most decreases. With some it is easer (as with SSK), with some it is more challenging as with sl, k2tog, passo. In this case you could do it exactly as it is written, but then with help of the left needle you move the “slack” one stitch at the time towards left until you have it out of the decrease.