I think we see three different BAT in the video: the S500, the S1000 (bigger), and Altaeros.
About the S500:
About the S1000, see above).
On the S1000 the diameter of the balloon is higher, and probably the same for the diameter of the turbine. That said I am not sure if the balloon is the S500 or S1000 at about 2:00. And also it works like a shrouded turbine, in such a way that the diameter of the balloon is far higher than the diameter of the turbine, the balloon being funnel-shaped. See also my experiment with a propeller within a tire compared to the same propeller alone.