Designing a desktop-view for a primarily mobile user base

I'm currently working at a startup where the only product we have right know is a "Mobile-Responsive" website.

In their own kind of bible, this startup defines "Mobile-Responsive" as creating the whole mobile web experience both in mobile-view and desktop view. Which means if you search for the website, you'll be looking at a mobile standard interface...on a desktop view.

I'm not sure whether this kind of approach is the correct for our customers. While it looks great and gives a good user experience, that's only if you're experiencing it with an actual mobile/phone/smartphone.

Our company uses this approach because 70-80% of our users are smartphone users. This reasoning is quite understandable, yet I feel the mobile-look desktop view approach is not correct.

What do you think of a desktop view with a mobile interface? Are there alternatives or best-practices for desktop site support for a primarily mobile user base?