In this case, the bookshelf is stronger than that poor screw. When attaching things, especially things with variable load and the potential for a lot of touching, you absolutely need to either drill into one or more studs (based on length of said item), or use the appropriately-rated drywall anchor (they are rated based on weight load). Both the anchor and screw must pierce the drywall, and the screw must be tightened so that it collapses the anchor back into the drywall. That’s what gives it the ability to hold up.