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.