It's not like this superficially either. That's literally what the word is.

finite - to have a limit, be bounded

The de- part is acting like it does in words like defraud. It's not a negative, like you might see in detox, where it means to remove something or undo something. Instead, it simply insists something has been done, not unlike the suffix -ify. You've been defrauded. In a manner of speaking, you could say you've been "fraud-ified".

You could say something that has been defined has been "finite-ified". The possibilities of what it could be were limitless, but you restricted them to something specific. You've made it finite. You've defined it. It is definite.