Who developed the "avformat-59.dll" that comes with FFmpeg?

First of all, you should know what DLL=shared libraries are.
DLLs are for Windows with extension *.dll but lib*.so on Linux.

What is a shared library?-Weblio

A shared library is a collection of components of a highly versatile program commonly used by a plurality of programs.For UNIX operating systems, it is provided as a file with the .so. extension and for Windows, as a file with the .DLL extension.

Also, the stories around the shared library on Linux should have answered some of Re9's questions in the past.

• Why can't I use the convert command when "rpm-qa | grep-imagemagic" displays the results?
• Why do I also install libX11, GConf2, and fontconfig libraries when installing ChromeDriver?

avformat-XX.dll is libavformat.so.XX on Linux, but the FFmpeg page on Wikipedia contains:

Includes libavcodec (video/audio codec library), libavformat (video/audio container library), libswscale (color space/size conversion library), libavfilter (video filtering library).

Also, since FFmpeg's official documentation page also has a page about Libavformat, avformat-59.dll may be considered a FFmpeg project deliverable.