In Godot almost everything is a Scene. A Scene is like a Prefab in Unity, except in Godot it is more advanced (you can have arbitrary levels of nesting, use inheritance, and other things).
Signals can be connect to instances of objects. An object can be a Scene, which could be a coin, your player, the HUD, or the whole level itself. I don't know what they video was about, and I don't have time to watch it, but this feature should be no problem.
On the main script (root node of the scene called "App"):
onready var count = get_node("VBox/Count")
var number = 0
func add_to_count():
number += 1
count.text = str(number)
On the coin or a button:
onready var app = get_node("/root/App")
func _ready():
var _id = connect("button_up", self, "handle_click")
func handle_click():
app.add_to_count()
I will upload an example project but the forum is having problems with zip files right now.