The current chain is not "Core". A lot of people are running non-Core clients which are compatible with the chain we're on. In the same way, Core could develop software which was compatible with the new chain as well if they wanted to do that.
And that's kind of the point, Bitcoin Segwit2x (the BTC1 client) is not compatible with the consensus rules.
Jeff Garzik is not coding the client that follows new consensus rules. He is coding a client that follows new consensus rules. No shift in power, because Garzik and other contributors do not have power over which client users decide to run. So users could decide to run a client which follows the same consensus rules as the SegWitx2 client we're talking about but is unrelated to it.
Also, how come they can't actually change the consensus rules without everyone agreeing to run their new client?