I wanted to try and do this without the plugin via a console command. For instance I can spawn a wolf by typing:

spawn wolf

Lets say I wanted to spawn the vomit noise (assets/bundled/prefabs/fx/gestures/drink_vomit.prefab)

What do I type into console to do that?

It doesn't run a command, it runs a method provided by Rust (which you can see in the code) to run an effect (provided by Rust).

This plugin utilizes that method to provide a chat command (not a console command) for use.

I see that it uses

EffectNetwork.Send

And the only way to use "EffectNetwork.Send" is from a plugin?

Yes, there are no native commands for that.