The distinction of malware is about who is being deceived. If a user willing installs on their own computer A some software to attack someone else's computer B,

The distinction of malware is about who is being deceived. If a user willing installs on their own computer A some software to attack someone else's computer B, that's not malware. If a user installs something on their computer that allows someone else, without their knowledge, to gain control of their computer, then that's malware. If someone breaks into a computer which they are not supposed to access and installs a rootkit that is designed to hide itself, that is malware. Obviously, this leaves some gray areas if a user is to go out and intentionally copy some botnet worm on their own computer -- since that software is primarily propagates surreptitiously, we'd still call it malware, regardless of whether someone once happened to install it intentionally. To your specific question, it depends entirely on whether the user is informed of what the software will do. If the user is aware that it's going to participate in a DDOS, or show pop-ups when browsing the web, or send their browsing history to Alexa, that's not malware. If, on the other hand, the user is told that they are installing a "nature photos screensaver" and its doing any of the above, then that's malware. And here we get into the debates about things like browser toolbars that were not very good at communicating what sort of spying they do when the user installed them. And it's clear to me that people rarely agree on where exactly to draw the line (and worse, usually argue adamantly that some borderline case either definitely is or definitely isn't malware). But nowhere in any evaluation of whether something is malware do I consider the effect on other people relevant, which was the original claim -- that this software was malware because it was abusive towards the web site owners who were having their ads blocked. Malware is entirely about software that intentionally causes the computer to do something other than what the owner or user intended it to do.