It looks like tabs were used instead of four spaces for each of the dash entries, which means you can't click the changelog button in the mod menu to see the changes.

Tabs were used, yes.

Why on earth is the parser different between the website and the game?

I'll fix it -_-

I think the website accepts any old text file, but the rules only apply for the game button.
There's an extension called "Factorio modding toolkit" for vscode that shows you errors in the changelog if you aren't using vscode / the extension already, super helpful for that.