The user interface needs to be re-structured.
This plugin works for QGIS 2.x
It is still pretty buggy, especially when it comes to any sort of error handling.
The plugin files SentinelDownloader should be copied into: ...\.qgis2\python\plugins\SentinelDownloader
The first time it needs to be manually recognized in QGIS by changing the QGIS plugin settings to inlcude experimental plugins.
If making changes, install the other experimental plugin called 'Plugin Reloader' so that you do not have to restart QGIS every time a change is made.