I haven't looked too closely at their method for cloning the application, but my guess is that the tools they suggest simply unpack the APK file, swap out the name, re-sign and re-zipalign the cloned APK. It's the same way you can modify or reverse engineer existing APKs using apktool, smali, and baksmali. In the context of the Android system, you're not creating multiple instances of the same app; instead, you have multiple installed applications that just happen to do the same thing with different IDs (after all, the Android system will not allow you to install two applications with the same application ID simultaneously). In any case, this is a rather unusual user case. Appium might be able to replicate this specific flow to creating a cloned APK and installing this new APK, but it will not be able to test the original application and the cloned application simultaneously.
Most Android systems only allow 1 application activity to be in the foreground at a time, so only the UI for 1 of the applications will be available at a time. I don't believe Appium currently has support for testing applications running on Android systems that allow multiple activities to be in the foreground simultaneously. As a side note, I've only come across a handful of devices that have the feature to allow multiple foreground activities; most devices and their systems don't have this capability.