Actually CME is using
CME CF Bitcoin Reference Rate for daily settlement and
CME CF Bitcoin Real-Time Index for marking to market during the day (basically the same methodology, par some details).
CME CF Bitcoin Reference Rate & CME CF Bitcoin Real-Time Index
CME CF Bitcoin Reference Rate (BRR) and CME CF Bitcoin Real-Time Index (BRTI), a standardized reference rate and spot price index with independent oversight are accelerating the professionalization of bitcoin trading. CME CF Crypto Currencies Indices have been generating BRR and BRTI rates since November 2016 with several bitcoin exchanges and trading platforms providing pricing data, including Bitstamp, Coinbase, Gemini, itBit, and Kraken.
So Gemini is only one of the 5 venue used to compute an average whose value is used to settle the future.
Chicago Board of Exchange (CBoE) is a different futures provider than the Chicago Mercantile Exchange (CME)