I think you overestimate the compexity of language translations. A creative process can help, but is not necessary. And if you use a translation website you actually do not know the tech used. Unless of course you use a site like chatgpt - and I am not even sure, if they use the actual llm capacity for translation. It is very likely, but it might also be, that they use the llm to understand what you want from it and use a different engine underneath for the actual task of mere translation to save computing power.
In it's core, a translation is not new content. The computer system does not know how freely it is allowed to translate. What you describe would be more accurately be called localisation and not translation.
If I upscale an image using an ai, or use a filter, that is not new content either. But all the new pixels were created using "ai". Maybe even the kind of ai that was trained on data. But I would not consider it "content produced" by the ai. And neither would I consider a grammar check or a translation as such.
Now, if you were to tell the ai prompt to generate a translation of your text and use the writing style of a certain author in that new language - or rewrite it in your own language in a different writing style - that would be new content.
In the context of the topic, it is about generated content. So I try to apply both words. It should not only be generated but it should also be content. A gen ai translation might be ai generated, but I do not consider it (new) content.
to not lie about the technology that I used to create my game
Fair point, but it is actually not about the technology used to create the game, but about the content and who initially created it.