Hi Martina,
yes, “Tobii Gaze SDK C API 4.0.3 Win32” is the right one. There you will find a developer’s guide giving the overall picture in the docs directory, as well as the C header files describing the implementation details of the C API in the include directory.
I also recommend taking a look at the code samples, because it’s difficult to puzzle together the pieces of what-needs-to-be-done-in-which-order without them. (Even if they are in the wrong language you’ll still need to do something similar in Delphi.)
You might also want to take a look at this: tobiisdk4j, it’s an open source java binding for the Gaze SDK.