“what do you mean modern computer browser?”
The Responsive Checker is using the visitor’s browser to render the mobile displays. So if I use Responsive Checker it will use my browser to render the website I am testing. In my case that means the latest version of Chrome for Mac. That’s what I mean, Chrome for Mac is a modern computer browser.
The real LG E400 Optimus L3 runs Android 2.3.6 (according to LG ). That is a 4 year old version of Android, with a browser to match. The current version of Chrome (47) supports way more things than the Android stock browser at version 2.3. Here is a comparison view: http://caniuse.com/#compare=chrome+47,android+2.3
The Responsive Checker is not letting me test how my website will look on the LG E400 Optimus L3. It is just showing me what my website will look like on Chrome with a very small viewport.
I hope that clears up why it is important to distinguish between modern computer browsers (like Chrome) and old mobile browsers (like stock Android 2.3 WebKit).