Well some do... baiting title maybe?
But the vast majority....VAAAAAAST majority play LOL.
There was even a study done, showing LOL had more players then world of warcraft at one point and DOTA2 never came close.
So I would probably rather watch a doc on that instead heh. Or how LOL influenced the construction of a stadium arena just for gaming.
It is very hard to find current comparison numbers, but those two games are far and away the #1 and #2 games played online. Saying "nobody" plays Dota 2 is ridiculous.
And the tournament numbers aren't even close. This year's Dota International prize pool will probably top $10 million. LoL has barely even reached $2 million. Dota is a lot more complex and fast-paced, which is probably why it is far more popular among spectators.
"Nobody"? That's a stupid assertion, sir, considering it's one of the most-played games on the planet, has better critical reception that League of Legends and has bigger prize pools than League of Legends.
If a documentary of League of Legends peaks your interest, you could always try and make it...
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While LOL developers do throw a lot of money (no, not influence, just buy things) to try and make their game look big, its competetive scene is far from being the largest one. Dota 2 while having lower overall player count also has larger competetive scene, rising above the previuos champion of starcraft competetive scene.
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Applied Science? All science is applied. Eventually.