I'd say think of them like http://www.wizards.com/dnd/images/oa_gallery/Shinomen_naga.jpg, and http://www.iol.ie/%7Etaeger/bio/nagodess_jp50.jpg, only golden, and probably have noticeable fangs (hence the "vampire" description). I'd assume they'd still look human-like, or else they would not be so accepted (the people of Tamriel are quite xenophobic).
Argonians and Khajiit are (generally) accepted, and they're quite non-human.
Personally, I've always pictured something along the lines of a hydralish with slight more human upper body features. Still viscous, fanged and scaled though. Also, in viewing the TES:V trailer, I got the idea that perhaps the Tsaesci are simply a type of dragon.
But we will likely never know for sure until one actually appears in an ES game. It's certainly fun for conjecture's sake at least.