It would probably be helpful to edit this post and shortly describe what Tyson's narrative about Mozi is. Then people who know about Mozi but did not watch Cosmos could answer. It won't help me, as I don't know anything about either Mozi or Cosmos, but it might help someone who can enlighten you.
Just watched the Cosmos segment on Mozi. The general facts are accurate, but they did make a few mistakes.
The Good
The Mozi does contain one of the first known descriptions of a pinhole camera or camera obscura. It's in the Canon II chapter of the text.
Mohism was a major philosophical rival of Confucianism. The Mohists did criticize the ritualism of Confucianism.
The doctrine of Three Models is a core concept of Mohist epistemology, and one of the three models is empirical (see the Stanford Encyclopedia of Philosophy for a more extensive description).
Some sinologists (Graham, Needham, Schwartz) have interpreted the philosophy of the Mohist disputers as rationalistic or "proto-scientific".
Qin Shi Huang, Emperor of the Qin dynasty, did suppress any philosophical school that competed with state sanctioned ideologies. This incident was called fenshu kengru (焚书坑儒, translated as "to burn books and bury Confucian scholars").
The Bad
It's inaccurate to imply that Mohism was more democratic or more "for the people" than Confucianism. Both Mohism and Confucianism advocated a hierarchical society led by a benevolent emperor.
Jian'ai (兼愛) is sometimes translated as "universal love", but the translation "impartial care" is more accurate.
It's a stretch to call camera obscura "film".
Counterfactual (what if?) history of any sort is questionable and most historians either avoid it or approach it cautiously. Speculations over what would have happened had the Mohists had won out over the Confucians or Legalists are pointless.