menschlechkeit is not gender specific. It refers to the trait of a human being who has good middos (menschen does not refer only to men, it is more like mankind, the collective noun, which is inclusive of women). At least, this is how I understand it.
If someone holds a door open for me, I make a point of saying thank you, and sometimes remark, “Nice to see that chivalry is alive and well. Thank you.” That always brings a smile from them.