Well, as the original post of the question (whether our motor is AC or DC), I was confused as well.
Here is a good article explaining the guts of how a brushless motor is driven:
ftp://ftp.ni.com/pub/devzone/tut/dcvsacbrushless.pdf.
The bottom line is how the ESC applies the current to the three motor wires at any point of time. In one scheme (ref to section "DC control/phase–phase connected motor"), the current direction in one wire can change over time, which is very similar to AC current!