Sometimes. Basically, this is the same as asking if glass is oven safe:
Generally, glass is oven-safe if taken from room temperature and put in a moderate-temperature, preheated oven. The key thing is to avoid temperature shocks (which will cause the glass to shatter). Some glass is specifically designed for oven use (either by being tempered or made of borosilicate glass). Often glassware will say if it is safe for oven use or not, and under what conditions—check the packaging or instructions it came with.
You also need to take precautions when removing glass from the oven. Do not set it on something that'll conduct heat away rapidly, such as a wet countertop.
Before heating glassware, inspect it for damage. Scratches, chips, etc. make failure much more likely. This applies to the microwave as well.
Note that non-glass parts of microwave-safe glassware may not be oven safe. For example, if it has a plastic lid, that should generally not be used in the oven (even though its OK in the microwave).
edit:
In response to your update, that oven is what would often be called a toaster or countertop oven. Those change temperature much more rapidly than a larger oven (which can be electric as well). So, generally, you'd avoid glass in them.
But, your glass says it can be used over a flame, from the freezer. So it's clearly one of the very shock-resistant ones, possibly borosilicate. I wouldn't expect it to be a problem. Just make sure to preheat the oven.
Also, since you know who made it, you can of course contact the manufacturer to confirm.
This will be a short answer as there is not much to say:
I have used cast iron pans on my glass stove top for about five years, and the surface does not show any scratches or marks. I have not taken any special care to protect the surface, and certainly have not polished the iron.
Best Answer
I don't think there's enough clarity in the video to answer definitively. So, a couple of critical points:
Of course, different types of glass have different resistance to thermal shock. But regardless of the type of glass, treat it gently and with respect. Just because it's designed to withstand abuse, doesn't mean there's any good reason to subject it to abuse, and plenty of good reason to use reasonable precautions. :)