I think "chivalry" would imply going above and beyond what someone would normally do -- or going beyond what is necessary.

In most cases, if the person in front of you doesn't hold the door open for you, it's just a minor inconvenience (unless your arms are full and/or you face mobility challenges). But when someone takes the time to hold the door open for another person (or for a group), it's chivalrous because it's showing extra care for someone.

I just don't see any reason why ithe behavior itself must be monodirectionally gendered (male-toward-female).