I would like to be able to use the WikiTocGenerate function for generation of the TOC for "non-standard" file types, however still following the Markdown syntax.

Currently, when calling the function I do get
wiki: No TOC support for filetype: vimwiki.wiki!
which also makes sense.

Maybe a little background. I use wiki.vim for keeping my notes in wiki, as I use taskwarrior for task management I also use taskwiki as a plugin on vim to handle taskwarrior data. With minor adjustments as in my local repository https://github.com/felixschurk/taskwiki/.
Now in order to have that plugin working as well as the normal wiki I created a custom file type vimwiki.wiki which is standard Markdown and also the files are stored as *.md files.

I assume that the WikiTocGenerate runs over the page and parses # blabla in order to generate the TOC, therefore I do think it would also work with a different file type, as the content in the file is still Markdown.
WikiToc is working, and there also the headers are parsed correctly.