In ESO, the opening cinematic shows Mannimarco killing others and the Souless One(the PC) for their souls. But is that where all souls go? Coldharbour? Molag Bal is the daedric lord of domination, so would domination over souls count as his sphere? Is that why the souls go to him? Or is there a special kind of soul trap/ritual that Mannimarco is using? It was my understanding that souls went to whoever they worshipped, or possibly sovengarde(for Nords) or the soul cairn for those caught in necromatic transactions. So why do they go to Bal's realm? They can't all be worshippers of Molag, certainly the Souless one isn't. So any ideas how it works?

I think it was discussed some time ago on the topic of soulgems, that black souls (souls under Arkey's Law) go to whomever created the black soul gem, so let's say a soul gem was "corrupted" and turned into a black soulgem by Bal, then the human souls within are sent to him. If the black soulgem was created by the Ideal Masters, the soul would go to them, and so on...

There's also to keep in mind that there's probably not just one spell/method to trap a soul, so yeah, he probably used a special spell made to send souls directly to Bal.

I also think it was said somewhere that Molag Bal was the one who originally created soul trapping as a form of domination.

Any links to that bit about Molag creating the soul trap? I'd like to give it a read through.

Imperial Census of Daedra Lords, IIRC, notes that Bal is only respected for the creation of the first soul gem.