One, Schopenhauer wasn't a pantheist. He was an atheist of a pretty strident and pessimistic variety. In the passage they're using he is dismissing it as a legitimate alternative to atheism; he's an opponent to the position. That is to say, Schopenhauer is (not necessarily wrong but) a relatively biased figure here. Better to let the pantheists explain their position than their opposition. This would be like arguing that atheism is the only rational position and supporting that by quoting Nietzsche when he said that God is dead.
Also, Literally the video goes on to explain why your position as articulate in 6:13 isn't itself totally compelling. And I would actually further argue that this video even while properly distinguishing atheism and pantheism also has a relatively attenuated definition for pantheism, as I explained before. It's simply not the case that pantheism if we're being rigorous is nothing more with God being synonymous with the physical universe.
Further, as they go on to explain panpsychism, even if you subscribe to the idea that pantheism only means that the the physical universe and God are synonymous, it would still suggest something meaningful about the universe. In other words the idea that the universe in totality is God suggests a number of things about the nature of the universe itself; things that that atheist wouldn't necessarily subscribe to. So... pantheists and atheists are characterizing the universe in fundamentally distinct ways, i.e. not merely a linguistic distinction.
Also, to be clear, somethings "sounds like smoke and mirrors" isn't an argument.
---the late great Donald Blake
I disagree with what you wrote. However, I’d like to focus on another critique right now. As a general writing tip, you can increase clarity and reduce reading exhaustion by eliminating unneeded fluff and writing at a 9th grade level.
Instead of saying, for example: “He was an atheist of a pretty strident and pessimistic variety. In the passage they're using he is dismissing it as a legitimate alternative to atheism; he's an opponent to the position.”
Say: “He was a strident and pessimistic atheist; an opponent to pantheism who dismissed it as a legitimate alternative to atheism.”