No, that part (cis) is a prefix and means "on this side of". And for "on this side of gender" to mean what cisgender is used as, is a newly agreed-upon thing in the evolution of LGBTQ culture.

That's not quite how a natural language like English works. There's a bunch of mess and idioms and "technically correct" is almost never how things start to get used in real life. Thus often it happens that whatever is the majority becomes the default, like for instance cisgender is a concept that almost never has to be used because 99% of people are cisgender. Not that it's not a valid term, it's just a term that's almost universally redundant.

I think he's referring to the difference of descriptive vs prescriptive. I mean, some english words and concepts just become standard without anyone trying to make them that.

Terms like cisgender or "they" as a pronoun on identical level to "he" and "she" is an example of trying to be prescriptive. You would never have to correct people with native level language skills on the correct use of these words if they weren't.