what keeps the pickup up would be the screw. the spring makes sure the pickup is held at a distance, then you can shorten the distance by turning the screw clockwise. you
could mount a pickup in the pickguard without a spring, but then any time the guitar was turned upside down the pickup would want to fall string-direction. hope this isn't as confusing for you as it is for me while re-reading it :icon_scratch:
ok, i'm literally this bored (the baseball game i wanted to watch isn't on TV) so here's a picture i took with my webcam. sorry for the crappy quality.
1. pickup mounting ring (same thing as your pickguard)
2. spring that keeps the pickup down
3. stew-mac thing that makes putting a pickup on a pickup ring a little easier
4. screw
hope that helps. i feel like it's easier to work out if you can see it all
and if your pickup doesn't have a screw hole in the tab then you got a dud really. the screw HAS to go through to make the thing work. and the tabs are threaded so that the screw doesn't need a nut on the bottom. i'd try to return, it's obviously a defect of some kind. it would be tough to just drill your own hole i think since it needs to be a threaded screw hole