All you have to do is use a blocking cap from the output of the mic to
prevent sending the DC supply voltage to the preamp. The schematic you've
pointed to has a 10uF cap between the output of the mic and the base of the
transistor, so that will do the job. So, the only adjustment that you need
to make is to connect the 1K resistor to the same mic pin as the 10uF cap.
IOW, connect the top pin of the mic in the schem to the middle pin, and that
will be the same as the 2 pin ecm that you have. Make sure that the cap is
on the transistor side of the resistor, though, so it blocks the DC (like it
is in the schem).
One caveat - I notice the whole thing is powered by a 12v supply. Most of
these types of ecms recommend a 2-10v supply voltage (oddly, it even says so
in the article). You may want to either use a regulator to drop the mic
supply voltage down to 9v, or use a simple voltage divider. Keep in mind
though, that the 1k resistor effectively sets the output Z; this will change
if you use either the regulator or the divider method.
One other thought - these ECMs can be had very cheap (I'm asuming you're not
using an expensive element here) so you might want to just go ahead and try
it with 12v, and see if it works OK. Where are you getting your mic element
from?