It does not protect you from Gemini losing or stealing the funds.
> This FDIC “pass-through” insurance may be available in the event that the Bank holding such U.S. dollar cash deposits becomes subject to resolution or similar proceedings by the FDIC.
https://support.gemini.com/hc/en-us/articles/205823016-Are-m...
Edit: Just curious, but how did you come to believe Gemini was FDIC insured?
It is on their website, but you have enlightened me: it won't protect them from grubby Winklevoss shenanigans, only the failure of the bank, and apparently only for USD assets. From the website:
U.S. DOLLARS
U.S. dollars in your Gemini Account may be held at Silvergate Bank, State Street Bank and Trust Company, JPMorgan Chase Bank, N.A. or Signature Bank and thus may be eligible for FDIC “pass-through” insurance, subject to applicable limitations. Please see the FDIC Insurance section of our User Agreement for more information.
EDIT: Oh, my copy-paste is from the very link you sent. Doh.