Now I have additionally ping-ponged the problem.

I also have Cygwin installed on my computer and I see diff.exe is also 
available in C:\cygwin\bin\diff.exe

If I rename the C:\cygwin directory to C:\_cygwin
and repeat steps from first post
then gVim is working fine also with v8.1_0366

Renaming cygwin directory back to original
and repeating the steps from first post
and gVim is producing the "Invalid diff format"
error.

I re-repeated the same thing with v8.1.0359 and it is working fine
with original c:\cygwin directory name.

I also see gVim has its own diff.exe file in
C:\Programs\Vim\vim81\diff.exe

Maybe something has changed in gVim code to not use Vim's diff but just calls 
the diff.exe from system and because Windows' PATH variable in my case is:
C:\Windows\system32;C:\Windows;C:\Windows\System32\Wbem;C:\Windows\System32\WindowsPowerShell\v1.0\;C:\Programs\GtkSharp\2.12\bin;C:\cygwin\bin;C:\Programs\Vim\vim80;C:\Programs\PuTTY

So cygwin before vim and it returns diff.exe from cygwin instead of gvim's 
diff.exe

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