I don't know how Google is internally organised, but maybe Google Labs does not have a dedicated legal team. And out of fear for possible legal implications, they just block it in EU. It's quite understandable, because the relevant legislations (AI Act etc) are all very new, not been tested in courts and due to the lack of stare decisis, you can't rely on a uniform application of the law in all jurisdictions, so they just block it. Frustrating, but I prefer they move fast rather than safe. And from their perspective, it means not releasing it in the EU.
NotebookLM is from Google Labs and was/is available from EU. It's problem with this specific chess project.