Solution
The package that installs the header files is libnidaqmx-devel. There are also a couple other packages that may be useful: libnidaqmx-doc includes the C API documentation, and libnidaqmx-examples contains the C example programs.
This convention holds true for other NI drivers as well. For example, libniflexrio contains the FlexRIO C API, but the header files are installed by libniflexrio-devel. If in doubt, try using the search function of your package manager (e.g. apt search <(package name>, or a partial package name)