I am not sure what system you are using, but is a standard C++ header file, so for most systems, the file using it, or including the header that is in would have an extension indicating it is a C++ file (normally on of .cpp, .c++, or .cc depending on the system). The header is basically the equivalent of the standard C header <stdint.h> with just a difference of what ‘namespace’ it puts some of the definitions into (which is a C++ distinction).
If the library was written for C++, it is unlikely to work well from plain C, but you can write a very ‘C’ like program in C++ as it is mostly upwards compatible. My first guess is that even if you fix the reference to cstdint, there will be other constructs in the header that isn’t plain C and will give you more problems. Maybe start by giving your file a .cpp extension and see if you can make that work.