I would change the text on the website. It gives the impression of emulating phones, which it does not at all do. It only lets me test a website in an iframe, so I can really only test what it looks like when rendered with my modern computer browser.
E.g. I can “Render My Website in” LG’s E400 Optimus L3. Except I can’t. The E400 runs an ancient version of Android, with a completely different version of the Android browser, that supports a completely different set of responsive CSS.
I see no reason why this website would be any better than Chrome’s build-in screensize emulator. And Chrome has the nice options of simulated slower mobile connections on top of it.