This is hogwash.
Don't believe it - there is not enough energy from the lens to power much of anything.
He calls his other bobbler the control, but he did not do the simplest control: take away the lens from the "lens powered" bobbler. There may have been enough charge stored in its battery, or enough random light from his flashlight to energize it. He should also have wrapped or covered the photocell of the bobbler photocell so that NO light could possibly have reached it. The beta and gamma radiation would have penetrated the wrapping.
This is a completely uncontrolled experiment as described and not valid. (Of course, the whole thing could also be an attention-getting intentional fraud.)
Take a look at this paper:
http://nvlpubs.nist.gov/nistpubs/jres/64A/jresv64An4p297_A1b.pdf
by somebody who actually knows what they are doing and has sophisticated measuring equipment as well as STRONG sources of radiation.
In figure 3, using a Cobalt 60 source (roentgens per minute) - WAY stronger than any lens!! see below - he gets currents of a few tens of nano-amps (billionths of an amp). That's not enough to do anything.
For instance, reported here:
Thorium coated camera lens, what kind of danger is there from using it? (x-post from /r/photography) : askscience ,
the rate from the back end of some lens was "measured the dose rate at the surface of the camera lens to be 0.48 mrad/h". (I think that should be mrem - millirem; a rem is comparable to a roentgen) That is a couple thousand time weaker than the source in the above NIST paper.