Michael Finkel writes in National Geographic:
Some scientists believe that one out of every two people who have ever lived have died of malaria.
The Wall Street Journal Article The Tenacious Buzz of Malaria by Sonia Shah author of "The Fever: How Malaria Has Ruled Humankind for 500,000 Years":
The malaria parasite has been responsible for half of all human deaths since the Stone Age
Did Malaria kill that many people?
No.
In the 2002 paper, Evolutionary and Historical Aspects of the Burden of Malaria [DOI: 10.1128/CMR.15.4.564–594.2002] the authors look at the history of malaria all the way back to pre-agricultural times.
They explain how bad malaria was at its worst point:
At some time during the 19th century, malaria reached its global limits. In absolute numbers and in the proportion of humanity now affected, malaria was exacting its highest ever toll of sickness and death. Well over one-half of the world's population was at significant risk from malaria. Of those directly affected by malaria at least 1 in 10 could expect to die from it.
Even at its most prevalent, the death toll from malaria wasn't even approaching close to half of all deaths.
The morbidity in the 20th and 21st century has dropped drastically, so it won't have changed since 2002 - this factoid is getting more and more inaccurate every year.
I can find no actual calculation to back up this claim.
In addition to those already given in OP's question, we have these other quotes.
Malaria may have killed half of all the people that ever lived (2002 Nature news article).
it is believed to be responsible for roughly half of all human deaths dating back to the dawn of civilization. (2005 academic article)
Others contend that half of all humans who have ever lived died from malaria (2009 Johns Hopkins Magazine article)
tiny malaria parasites, transmitted through the bites of infected mosquitoes, are thought to have killed half the number of people that have ever lived. (UK charity webpage)
None give a proper citation as to who is doing the "believing", "contending", or "thinking".
The closest I can find to a proper analysis is this informal analysis by a blogger, whose conclusion is:
We’ll never know for sure, but based on my reading I think it’s possible.
Based on all this information, my guess is that this is probably an academic urban legend, perhaps first started by that 2002 Nature news article. This does not however mean that the claim is necessarily false; merely that no one has actually ever done the proper work to back it up.
