Without watching the video or knowing about the campaign, I would suspect that the reason they had difficulty was because they were so heavy infantry-centric, and that's just not suitable for hotter climates. You'd get cooked wearing all that metal in the mid day heat.
I know they had a lot of success in other hot places like Egypt and north Africa in general, along with Syria and Jordan. Plus southern Europe itself can get pretty warm in the summer. But I would think that Sudan is hotter still than those places. And more humid too.
Generally wherever they struggled it was because of unfavourable geography and climate which acted as a force multiplier for their enemies and as a force divider for their own system of military organisation and equipment. The dense forests of Germany, the Iraqi desert, and it would appear the lands of Sudan as well.
This is equally true for everybody, though. The Persians before them were all conquering with their foot archer and light infantry system, until they got bogged down in the high mountains of Greece and got overpowered by the Greek heavy infantry. The Mongols were unstoppable everywhere except in the tropics, where the extra moisture in the air from humidity and the daily heavy rains made their horse-archers completely ineffective, because water dissolved the animal glue used to bind their composite bows. They had such a problem with humidity and rain in Vietnam that they never attempted another tropical campaign afterwards, so they stayed out of India and Africa altogether.
This is why I find ancient and medieval military history so interesting, because the military systems were a direct product of each individual culture, and because all of these systems had their limits which would be exposed once you got into a part of the world that had a completely different climatic and geographic environment to your home. There was always a trade off: if you're really good at one thing, you cost yourself being good at another thing. And nobody could master all the range of skills that were needed.
You don't get this diversity or this link between culture, environment and military systems in modern warfare. Everything is basically the same, so it's a lot less interesting to think about.