Interesting. I don't think that would be possible - the technique shown here relies on a mirror to get interferometry between the two light paths. I can't see how interferometry would be available to soaring birds (between its two eyes, perhaps?). Although nature has come up with some very surprising and impressive inventions before, so I might be wrong.
I would guess they're just very good at spotting the conditions which lead to thermals.
EDIT: of course, you can directly see thermals via the shimmering / "mirage" effect. It's normally obscured by the background noise, but maybe soaring birds are attuned to that. That's much more plausible, but a different effect to that shown here.