Using the static version I get undefined references to the WebUI function calls and the dynamic version just results in the same file format error as in my original post.

Here's the entire gcc command:

gcc -Os -Wl,-subsystem=windows src/*.c -I"include/" -L"lib" -lwebui-2-static -lws2_32 -Wall -Werror -luser32 -static -o webuiWin

I guess you are mixing libs ABI, so make sure you are putting the Windows GCC library version in lib folder.
On the other hand, you can easily re-compile it from source:

git clone https://github.com/webui-dev/webui.git
cd webui
mingw32-make

Then copy dist\webui-2.dll into your lib folder.

Using migw32-make results in:

GNUmakefile:60: Extraneous text after `else' directive
GNUmakefile:68: *** only one `else' per conditional.  Stop.

Resolving all issues results in:

process_begin: CreateProcess((null), uname, ...) failed.
mingw32-make: *** No targets.  Stop.

Using make:

MAKE Version 5.2  Copyright (c) 1987, 1998 Inprise Corp.

** error -1 ** deleting release

What version of MinGW you have? And OS.
Normally building from source should be fine.