Well, I'm glad that somebody finally said it. They and them never have and never will be pronouns. (Btw, I have absolutely no idea why this video isn't at the beginning.)
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But there was no gender pronoun for a specifically identified individual in that sentence, so your attempt misses the mark.They and them have been singular pronouns for centuries. It's called the singular they, and is used to refer to a person whose gender is unknown or unspecified.
"Someone is coming up the street, and they will be here in five minutes."
Perfectly normal.