The main problem is, that you open your MainMenu Widget in the FirstPersonExampleMap and not in another Level.
To show you what realy happens when you start the game is the following:
It loads the FirstPersonExampleMap map. This is configured in Project Settings > Maps & Modes > Default Maps > Editor Startup Map.
It loads the MainMenu widget as configured in the FirstPersonExampleMap Level Blueprint (with the BeginPlay Event).
When you now click the Play Button it loads the FirstPersonExampleMap again. This reload of the map triggers the BeginPlay Event of the Level Blueprint again executing the step 2. from above again.
This loop makes it look like nothing happings but this is incorrect. To fix this you have to create a new Level i.e. MainMenuLevel. Configure this as startup map in the project settings and let it load the MainMenu widget and remove the MainMenu widget from the FirstPersonExampleMap. Then everything will work as you intend it.