You are mostly correct that the original version of MRT was limited to Flashback removal, but they added a few other bits of malware in latter versions. It was originally included in OS X Security and Java Updates along with the standalone described in the document you found. It was a one time scan for known files installed by Flashback (and others later on) which would inform the user if it found anything, but silent if not, and deleted itself after that scan.
The new MRT that is included with El Capitan has not been documented by Apple anywhere that I have been able to find, which is not unusual for matters that involve security. For that same reason, I am reluctant to provide all of the detail in what I have been able to figure out. Best that malware developers not have too much information and attempt to defeat it.
As far as I can tell, the new version of MRT performs the same actions as the original, i.e. it looks for selected malware/adware files in known locations, removes them and notifies the user. The major difference is that it performs these scans at each startup, rather than one and done. It is updated in the same manner as XProtect when you have "Install system data files and security updates" enabled in System Preferences->App Store. The current version is 1.8 which was available on or about April 28. To see if you are up-to-date check <Option>-->System Information->Software->Installations and look for "MRT Configuration Data". Updates tend to come out when XProtect adds a new malware/adware signature since XProtect looks for installers and MRT looks for files already installed. I have a pretty good idea what it's looking for, but again I will only say they bear a strong resemblance to files installed by some of the most recent software on the XProtect list.