You cannot do that.
From the question’s title, it kind of seems you think WooCommece is not a plugin, and you install it using a plugin, but the thing is that WooCommerce is a plugin.
You are following a guide called Template structure & Overriding templates via a theme, doing that you are only doing so, not installing WooCommerce without a plugin. (sounds funny when you actually say that)
There shouldn’t be an issue if you simply install it and use it like the rest of the word.