What is Shariah?
I understand your point although is not the way I personally understand it.
My belief has been that Shariah is one (the second part of your description), the whole set of rules (legal stuff, family, everyday rules, etc).
So my understanding is that to be a Muslim you have to believe in all of Shariah rules (the ones from the scriptures)
Maybe you don't have to believe or accept the human additions to it.
So at the end and based on the concept that Shariah is ONE big set of rules then I'm inclined to believe that Shariah cannot be separated from Islam, they are one and the same.
If you don't follow Shariah then you're not a real Muslim.
I thought my previous answer should've made everything clear.
For your better understanding, let me make this sound easier as I understand it.
There are two "Shariah"s -
1. "Shariah of Man" - Combination of Quran (literal understanding), Sunnah and Hadiths, but I would say mostly Hadiths. They made law from this to meet their needs. Legislation.
2. "Shariah of God" - Only Quran. What God tells us to follow. A way of life. Can be made into Legislation or not.
So, one has to obey "Shariah of God" (which is much more spiritual than physical in my opinion) but not necessarily "Shariah of Man".
As I said earlier, "Shariah of Man" has been corrupted and twisted heavily to meet the need of those who implemented it.
So No, "Shariah of Man" is not a requirement to be a real Muslim.