Compiling libwebp.dll requires Visual Studio IDE.
Download the latest source for libwebp here: https://storage.googleapis.com/downloads.webmproject.org/releases/webp/index.html
Extract the source to the .\lib\ folder (or any other folder)
Open x64 Native Tools Command Prompt for VS, navigate to the root directory of the libwebp source and run the command below to build:
nmake /f Makefile.vc CFG=release-dynamic RTLIBCFG=dynamic OBJDIR=output
The libwebp.dll binary should be available in .\output\release-dynamic\x64\bin\libwebp.dll
Move the compiled binary to the .\bin\x64 directory of this project.
Set build target to Win64 for project in Delphi and build.
Output is in .\bin\x64
Follow the same instructions but use Developer Command Promt for VS and move to .\bin\x86