Early ARPANET logical maps (from 1970 onwards), as well as the geographic maps (note the UTAH spur in the 1969 map), show that it was not a full-mesh topology; there must therefore have been some kind of routing.
J. Noel Chiappa's website references a few early documents that talk about the specific implementation of routing at that time:
And you can also find what was the predecessor to that document – BBN Report No. 1783 from April 1969, only slightly later than the original proposal that was mentioned in Internet Daemons:
Eventually the routing algorithm was replaced with a different one (from distance-vector to link-state) – which was still happening in the NCP era; no IP or gateways yet:
This topology lasted for a long time – even with TCP/IP in place, ARPANET still relied on IMP routing (with the original Host/IMP addresses becoming practically "layer 2" addresses underneath IP, so that the entire IMP-based ARPANET appeared as a single flat class-A IPv4 network, with 10.hh.hh.ii
addresses being directly mapped to underlying Host/IMP addresses); IP gateways were only needed between the IMP-based ARPANET and other networks.
(I don't have any sources handy, but when I was reading about the 'HELLO' routing protocol used by NSFnet, it was mentioned that the resulting "flat L2 network" appearance of the ARPANET had caused difficulties for the development of IP-layer routing protocols, as the entire network appeared as a single link (interface) yet had varying costs to different destinations – and even these days, routing protocols such as OSPF can't represent that easily.)
More information (post-1973) can be found at:
Don't forget to read the IEN series of documents; they document a lot of the "early IP" evolution in-between RFCs (such as TCPv2 and TCPv3, before it was split up into TCP/IPv4).
Keep in mind that ARPANET was not the only network in existence, and the notion of "gateway" (in the sense of a router) existed in other networks as well, even if wasn't necessarily called that way. For example, Xerox's XNS – which IPv4 took some inspiration from – also had routers or gateways before ARPANET did (IP even took the RIP routing protocol from XNS).