I think my examples fit with what Forest said in the video. Can you explain why don't?
And can you explain why you think a "tomboy" climbing a tree is an example of this?
Traditionally, women have worn their hair longer, and men have worn their hair shorter. Those have been part of the gender identities found in our culture. Remember when everyone was all upset that the Beatles had "long hair?" Why do you think that was?
Similarly, it's been traditional for girls to express themselves wearing pink, and for boys to express their gender identity by wearing blue. Boys who have worn pink have been traditionally views as "girly" types in our society (thankfully that is changing).
Those things are recognized in our cultures as "things girls do" and "things boys do."
Notice how your example of gender identity was for a "tomboy" to climb a tree. Would that be because traditionally, our culture views boys as the ones who climb trees, perhaps?
I believe that gender frequently operates independently from sexual identity.
As I recall, the reason we're focused on this exchange is because I'm critical of the video you provided. While I found much to be critical of, in the video, I focused on this direct quote:
"Gender is how an individual organism expresses their sexual identity in a cultural context".
It strikes me that you're defending the video you provided, correct? In that context, I don't think that an example like "long hair" has anything to do with sexual identity. Do you?
So again, can you provide an example that backs up the video's claim?