This is a bit trickier than it seems.
1. The $level is indeed missing as a parameter in the tutorial and should be added
2. The $navtype should be 'nav-user' instead of 'user'
3. This is a whole section, as it is more complex than the previous ones:
Considering you're playing with layers and trying to learn, which is the purpose of any tutorial, I'd say it is not the best tutorial. A tutorial should aim at exploring things that are as common/standard between themes as possible. I'm saying the tutorial could be improved because themes usually want to provide a way to register/login which fits the theme's author taste. This results in the author playing with the links to those features.
SnowFlat, which is now the default theme, is no exception. Check this method. If you take a look at it you'll realize that the login button is already gone (unset) in there. So why is it still being displayed? That's because a custom login button is added right above it, which is the <form> that is output in the previous statement.
So if you want to remove the Login button in SnowFlat you'll have to modify that method and maybe even qam_user_account(), to make it look good.
The thing to understand here is that everything is chained in this order: base theme, theme and layers. So you can't really assume anything at a layer-level, as themes (and other layers) can change the context that you give for granted.