How the use of the word screw (or f**k) came to mean forget about it or disregard it or treat it with contempt, I do not know. I find it unfortunate that what is meant to be an act of love within the confines of a committed relationship has become a curse word. If copulation is such a disgusting thing, why don't we say, "Rape it!" which is truly disgusting and worthy of contempt.
In rhetoric, there is a figure called procatalepsis, which is a way for a rhetor to anticipate an objection his audience might have and then deflate the objection before going on to the point the rhetor wants to make. For example,
"Those in favor of capital punishment point to it's being a deterrent to crime. This is patently true in that the murderer whom the state kills will never kill again. What these people fail to realize, however, is that if the state somehow got it wrong, and the "murderer" turns out to be innocent--not guilty, then there is no way to undo the tragic and premature ending of a life."
In the essay to which you refer us, "Screw Motivation, What You Need Is Discipline," there is what might be called a mini-procatalepsis. The argument (or line of reasoning) which is being debunked with two short words (viz., screw and motivation) could be summarized as follows:
"Discipline, some folks say, is too harsh a word, and it conjures up something unpleasant and hard to bear. They say we should rather use the word motivation to express how a person gets something done. I say poppycock. Claiming that one has to wait until he or she is motivated to do something is merely an excuse for not doing it, not to mention causing disrepute to a word which used to convey backbone and stick-to-it-iveness in the absence of motivation. In other words, don't wait for motivation, just dive in because something needs to be done--NOW, not later."
At this point you likely see how economical "Screw motivation, what you need is discipline" is. Seven words sum up very well what took me over 100 words to explain discursively. (By the way, the word poppycock is a less shocking expression than "screw it.")
I applaud economy of expression, because sometimes, in some circumstances, that is the way to go. It can also be a lazy person's way of deflating an idea without real proof, logic, and persuasion. Any rabble-rouser can scream, "Screw the establishment." A person who is interested in true, lasting, and ethical change, however, will take time to formulate the best possible arguments to support his or her point of view.