The link you posted does mention fdic but it says Gemini’s deposits are fdic insured (probably true as what kind of a crazy company keeps cash in uninsured accounts). Definitely shady of them to word it like that as it’s likely meant to confuse and mislead. But again, pretty easy to validate and disprove before sending any funds.
I hope you get something back and I guess the good news is that you only make this mistake once in life and teach everyone in your family how to avoid.