The only thing wrong in the video: Reach Hacks don't exist.
From my research, it appears that reach hacks did indeed exist, but it was in Beta. Any clients at the time that had reach would just attack one block sooner, but deal no damage —just the knockback.
There are some hacked clients were you are able to change the values of your hit box for Force-field and Killaura. If you set the value to three, the client would attack an enemy three blocks away from you; if you had it set to six the client would attack an enemy from six blocks away from you.
However, MCGamer has No-cheat + and will most certainly kick anyone who can hit anyone within six blocks away making it one way or another not possible in MCGamer.