I saw this report and video just now, and holy cow! I hope she's OK!
The article is a bit misleading in the sense that it's saying that "Gravity wins". It really has nothing to do with gravity, but rather, conservation of momentum.
Say the guy has mass M, and the woman has mass m, with m < M. For simplicity sake, let's assume that they both had the same velocity (but in opposite direction) before the collision
Momentum before collision is
Mv - mv = (M-m)v
Momentum after collision is:
MV_f + mv_f
(I'm not making any assumption yet on the directions of the velocities after collision.)
Applying the conservation of momentum, we get
(M-m)v = MV_f + mv_f
This means that mv_f is
mv_f = (M-m)v - MV_f
v_f = (M-m)/m * v - (M/m) V_f
Now, from the video, V_f (the velocity of the man after collision) appears to be in reverse, but very small, so V_f is negative, but small. So the 2nd term in the last equation is negative, making the equation to be
v_f = (M-m)/m * v + (M/m) V_f
Now, if M is substantially greater than m, M/m >1, and so (M-m)/m is also >1.
This means that v_f, the velocity of the woman after collision is greater than v, the initial velocity. She will recoil after collision with a greater speed than when she came in. This is what happened in the video.
One can also add another assumption of elastic collision, assuming the exercise balls didn't absorb too much energy in the collision. But I think the point has been made here. :)