The "Non-people don't count ... or do they?" section (YS232) gives some guidance here, but it's not entirely clear-cut.
Distilling it down, my take is that the First Law basically governs using magic to seperate a living soul from a mortal body. In particular, it does *not* apply only to humans; it would be better to use the terms "mortals" or "people" instead. In the vanilla Dresdenverse, this largely means humans. In your world, however, that is less true. Perhaps it would be easier to define who the First Law doesn't apply to. That would be pretty much anything that is monstrous, supernatural, of the spirit world or underworld, or of the Nevernever. Either way you end up with some judgement calls, which you as the GM (or your group as a collaborative effort) should try to nail down, preferably before the issue comes up.
My own take would be that in a D&D setting, humans, dwarves, elves, halflings, and the other basic player character races would count as "people". Monster races, outsiders (even native outsiders or planetouched like Aasimar or Tieflings), and anything supernatural would not.
It's probably best to keep in mind that the Laws govern what you can do to (mortal) people. In the Dresdenverse, this is often simplified to humans, since there are not any non-human races after you throw out everything that's monstrous, supernatural, Nevernever-ish, etc. In a D&D-style setting, however, the basic player races (elves, dwarves, etc) should equally count as people. The more outsiderish races such as Tieflings and Celestials, of course, would not.