From a starter's standpoint anyway, for physical sadism, a warped form of empathy is mine. I don't understand pain in the conventional sense, so seeing another in pain gives me a tickle similarly to light forms of pain inflicted on myself, except it feels more... indulgent, controlled, powerful. Even watching a character act out pain well in a movie, or just seeing some random stranger hurt themselves has me struggle not to let out some sort of response, be it a light moan of ecstasy or a laugh. Crow tends to do an elbow nudge when I look a little too happy about another's suffering as a subtle reminder that yes, we are in public, and people if I'm not careful will stare.
Struggle is also one of the prettiest displays a person can express. It's so... honest, so expressive, so real. It also stems from an appetite, an itch, it feels good to watch another person writhe. If the person's into it, it also makes their eyes express a needy vulnerability, a dilated, dreamy-eyed look of want that allows for further action. Even penetration triggers a similar interest, that look they give as entry begins, it's not that different from other forms of infliction. Defiance makes it better too, as then it feels like a challenge, progressing them towards their inner truth, their inner weakness, the side of them that lacks all those masks, all those barriers, and is truly the core of a human creature.
I had no abuse in my childhood personally, so I don't really fit your theory. It feels more like a matter of passion than proxying a past abuse.
For emotional sadism... I mean come on, it's great. What's not to like?