I'm currently putting together MVPs of the difficult UI aspects of my system, because those are the parts I'm worried about. The back end is actually pretty straightforward. The UI stuff is the stuff I want to get in front of users for review.
After that, I need to do some technical MVP for proof of concept, to prove to myself that my assumptions about certain data patterns are actually correct.
The important thing, though, is to get to where I have working code I can show others to get feedback, even if that code isn't anywhere near complete as a marketable product.
Testing your UI is what most people would call prototyping, though. You've already decided on what you want to build, just not what the interface to what you're building should be exactly. An MVP is for deciding what to build or whether to continue to build.
Or more importantly, what version of what you build will your customer pay for/use - i.e. what will add value such that it would change their behavior.
An MVP will tell you if it's even worth doing that UI design in the first place. If you can get people on your site going "I'd pay for this if only it didn't suck to use" then you have an MVP that's validated you have a market.
If you have a great to use product and can't get people to stick around on the site, you've wasted a lot of effort.
A UI is the M in the MVP. The back end would be a fair bit of work for nothing very exotic. I can test certain assumptions about the front end using public data without all that effort. Technically, it's probably a demo, not a true MVP, but it should tell me a lot about what works and what doesn't, and it shouldn't be too hard to expand into a true MVP afterward.
After that, I need to do some technical MVP for proof of concept, to prove to myself that my assumptions about certain data patterns are actually correct.
The important thing, though, is to get to where I have working code I can show others to get feedback, even if that code isn't anywhere near complete as a marketable product.