So using Markdown or something similar disqualifies? Even if i write the HTML template and generator script myself?

If you look at the submission form, he excludes "website builders" which I think would exclude things like Squarespace, Wix, etc. I suppose if one of those builder tools let you use Markdown, that would not qualify, but if you are using Markdown with something like Hugo or Jekyll, that seems legitimately "handmade" to me, but I don't operate that site. :)

What about a handmade template for a CMS?

It depends. Did you write the scripting language?

By the spirit of the thing, Markdown ought not qualify