Nope, that’s not what is says. Please read again: ““Homosexual, gay, lesbian: A person who is attracted to people of the same gender.”
Gender is not the same as sex. For example, a MTF trans person and a cis-man are physically attracted to each other. They are a straight couple, even though they both have the same sex.
The author claims this is simple, but it’s not. It is also not too complicated, but it does take more effort than when the word for man meant having a penis and women meant having a vagina — and that was it.