> Is TCP/IP really what makes the internet the internet

Yes, because the Internet is the Internet because it's a network of networks, all sharing the same protocols, all routing data among each other via gateways using packets. Networks existed before Arpanet, before PLATO, but it wasn't possible to cheaply interconnect networks and send messages end-to-end before TCP/IP.

Removing TCP/IP and the concept of the gateway from what it means to be the Internet doesn't mean PLATO is first. It means some even earlier computer network is first, and PLATO is still a footnote in the history of the Internet.