When they do that, they are focusing on the English subtitles and effectively filtering out the Japanese. If they tried to hide the subtitles and only glimpse at them occasionally they would start to see gradual improvement. Many people won't because they'll find they suddenly can't understand most things and it becomes exhausting. by that that's what it's like when you are really learning.
That being said it's still a slower way to learn because the language in anime is quite removed from a typical real conversation you will get in to.
I believe Krashen's theory is easy to misunderstand. If you only take a brief look at it you may think it's over simplified. The theory isn't just input in the sense that you've at least got the language going in you're ears. The "comprehensible" part means that you are comprehending via the language, using context to fill in the blanks. I don't think you learn from outputting language, but outputting is essential for producing the ideal comprehensible input.
For example, BTBurke's third point is to ask questions to a native speaker. Note that here, the native speaker is doing the speaking, and BTBurke is learning when listening, not when asking the questions. But asking questions to a native speaker like this and refusing to give up and go back to your native language engages the human brain in a way that simply watching some videos doesn't, and provides important context. Krashen calls this compelling input.
In BTBurke's first point, they say production is essential, but I think Krashen would say this so-called production (talking to native speakers) is really just using production to get ideal comprehensible input from native speakers when you listen to them speak back to you.
As for the 5 minute minute presentation. I would say that this 5 minute presentation is mostly just testing one's current ability, but the preceding the presentation there would be hours of looking up (and inputting) sentences that you wish to say rather than learning randomly, and that's where most of the real learning occurs.
I apologise for the "It's both right and wrong at the same time" kind of answer. In summary I believe BTBurke is a fantastic language learner, but if you look closely at what they are doing, you'll see they are providing themselves with plenty of comprehensible input, and the production/output as actually a more minor part that facilitates this input.