I am working on a project that uses Google Translate API. The premise of the website is this: Translate the beginning text to many different languages, and at the end, translate it back to the original language, and it should say something very different. It is the classic game of telephone using Google. I've read through the terms for the API, but I couldn't quite get an answer on if Google would allow me to use the Google Translate API in this way, on a live website or application, for entertainment.
Back when Google still had the free Translate API there where terms which would have made this against the rules as the terms stated that it was for the purpose of translating source content to an alternate language for end users to be able to read or for translating user content from their source language to the site language. Since the depreciation of the v1 API and elimination of the free translate API the terms are now a little more lax in the sense that as long as what you are doing does not go against Google Terms of Service in general you can use the Translate API.
As such based on reading the Google Terms of Service and the Translate terms of service I can not see anything that would prevent you from being able to do this however you need to accept that the Translate API is a paid service now and you would not be able to do this for free. The only free translation service that Google still offers is the Google Website Translator gadget but this would not do what you are wanting to do as while it changes what the end user sees it still saves the original source text and any changes to the translated language is performed based on the original source text and not the translated text.