I see where this is going roughly means I know what is going to happen. It is used to indicate that you can predict how something will change, where it is headed, or the outcome of something. Of course, your prediction doesn't have to be right.
In the video, the lady is saying that she knows what will happen. However, we can't really know what her prediction is because she doesn't say it out loud. Maybe she predicts that her logical answer ("20") is correct because respondents are expected to answer "5". Maybe she predicts that her logical answer will be wrong because it's a trick. Maybe she realized that the correct answer is "no time at all because it's already built". We can't really say.
As for another example, imagine a superhero and a supervillain. The hero faces a dilemma: save A or save B. A is on one side of the bridge and B is on the other. There is only enough time to save one, according to the the villain. But you might say I see where this is going. The hero will do X, Y, and Z in order to save A and B. In other words, you predict that the hero will be able to save A and B despite what the villain said.