Before fixing the problem, it helps to understand the mechanics behind it. A (Dynamic Link Library) file is essentially a set of instructions that multiple programs can use simultaneously. The steam-api.dll file is a specific component used by Steam to handle game licensing, DRM (Digital Rights Management), and communication between the game and the Steam client.
Remember: never download DLLs from third-party websites. Always source from Steam, the official HD Project site, or your own verified backups.