Steps:
It looks like this:
The patch file is valid and I can use unix patch to apply it successfully (with some line-ending tinkering).
I'm on Windows 10 and TortoiseSVN/TortoiseMerge 1.9.5
The problem was that TortoiseMerge was maximized. There's a floating window on the left.
Unmaximize the TortoiseMerge window and you can see the file selector window. You can select files in that window to see them in the diff view and there's buttons for applying the patch.
It should look like this: