Gateways

The name gateway sounds special. Yet it's just another IP of the subnet. It need not be .1. This IP is given to a router. The router then links this subnet to other networks.

mental model for gateways

A router joins the network. This extends the data link layer of the subnet.

That's exactly why broadcast messages reach the gateway interface too.

Software behind Gateway

Behind every gateway, there is software. It handles and routes all the traffic in and out.