I would say the O-ring does not belong with that kit. Looking closer at a number of these pen kits, is there an O-ring at the base of the nib where it connects to the body? See attached picture.
I looked at 3 different sites instructions and none have an O-ring listed in the parts. One of the sites, Williams Pens, even shows the kit and does not have an O-ring in the parts.
One possibility though, does the O-ring look to match the one that is in the ink converter in your pictured parts?