You're on the right track. Concrete is great at resisting compressive forces, steel is great at resisting tensile forces, combine them and you get the best of both worlds. Now in the video the test that he showed for concrete is used to determine compressive strength, so modern concrete should be good at this too. We don't calculate the strength in kg but in Newton per square millimeter. This way we can compare samples of different sizes. I'm guessing the ancient concrete cube has a length of 100 or150 mm? At 80 tonnes this would mean a compressive strength of around 60 or 27 N/mm2. Which is around the same as some concrete used today. We can actually produce concrete with more than 100 N/mm2 but this is rarely done because it's quite expensive. With modern concrete we can reliably calculate the resulting strength of the mix, so we usually just select a mix with a little bit more strength than is actually required by the structural engineer. We could use stronger concrete but that would just be a waste of money. My guess is, that they deliberately chose a weak concrete for the video or added too much water to the mix.
