If someone says "faggot" it does not mean they're homophobic.

Look, I understand this. This is not what I'm saying.

The word in and of itself breeds homophobia. Using the word does not mean the user is homophobic, but using homosexuality as an insult normalises the hate of gay people. It implicitly promotes homophobia.

Whatever you want to believe about what the word means, the word definitely implies the receiver is gay. If you were to ask someone "what does this word mean?", I'm certain that "gay" would be part of their answer.

I'll restate the example I used in my previous post. The word "gay", when used by schoolchildren, is used as an insult, not to mean that that person is gay. However, the word "gay" does also mean homosexual. The children that use "gay" as an insult aren't necessarily homophobic, but they're not exactly cognizant of the implications of using a sexuality as an insult. I've heard plenty of anecdotes of actual homosexuals who were called "gay" at school having a harder time accepting it.

He even stated in the beginning of the video that he is not associating the word with gay people.

Sure, but the fact he needed to make that clarification means that people do connote the word with homosexuals regardless of context. If it only implied anything about homosexuality in a specific context, he wouldn't need to say that.