How does WiFiKill actually work? There is a program for Android, WifiKill, which disables wifi internet access of some neighbor peers connected to the same wifi AP. How does this program works? ARP poisoning or some other techniques?
The app's author himself explains how it works at the top of the second page of that thread you linked to:


  It's the same idea as FaceNiff (I'm a developer of it also), basically
  it sends ARP Reply's to all of the devices in the network fooling them
  to think that your mobile is router. And then all of the devices try
  connecting to network THROUGH your device... and you just drop every
  single packet from them. In this version it's just dropping packets
  but maybe later I'll try adding some sort of primitive REJECT target.


And slightly more on page 5


  
    Originally Posted by Jufjufjuf 
    
    Is this using an arpspoofing attack? Just wondering if there was anyway to send out de-auth packets through android like airdrop-ng?
  
  
  Yes, it's using arp spoofing. I suppose there is a way to send deauth
  packets but it would require modifying kernel drivers for wifi card.
  AFAIK it won't work out-of-the-box because most of android wifi
  drivers don't allow packet injections and even changing the mac
  address of the NIC is super-difficult in a lot of devices.


As far as tools for desktop OSs go, there are a few that will do this kind of thing, MDK3 seems to be a popular one for doing this kind of thing.