When looking at a device's routing table, can you tell whether it is a gateway device between some networks or if it is not a gateway device?
You can’t tell. There will be entries for the local networks, but there may or may not be additional routes.
If the device is configured to forward packets from one interface to another, it’s a good bet someone is using it as a gateway.
You can do a
show ip route (on cisco devices) or any other similar command on other devices and you will get the gateway of last resort for the specific network.