I think I see the issue.
The difference is that Sombreve’s game (Dawn of Corruption) runs from an external site published with GitHub Pages, where it sits right at the document level — the page that loads is the game itself.
When Curse of Something loads in the browser, even though it’s a full-page interface it’s using the itch.io loader, which means the game itself is loaded in an iframe embedded in the page. (The iframe takes up the entire page, but it’s still there.) I suspect the browser translation can’t access the iframe content to translate it.
If you’re using Firefox, when Curse of Something loads you can right-click anywhere on the page background and choose This Frame > Open Frame in New Tab/Window to pop the iframe out of the surrounding page and load it on its own.
Other browsers don’t have that option, but the URL that Firefox loads when you open the iframe in its own tab is this one, currently. (Note that the URL may change or not be valid for everyone, maybe it’ll work maybe it won’t. The Firefox method is more likely to work correctly long-term.):
I’m curious whether you have any better luck activating translation when the game isn’t loaded inside an iframe. I suspect you will.