This projection looks to be either Robinson or Winkel-Tripel – both of which roughly do preserve area ratios.
Which is why all Wikis use these projections, or variations thereof, as standard base map (and it looks as if he just took at Wiki base map and colored it)
Of course, the internet is fantastic for pedantic nitpicking.
While we're on the subject of map projections, I would suggest taking a look at the Authagraph projection.[0] It preserves the size and shapes of all the continents while simultaneously giving the viewer vertigo.
Yeah that's pretty glaring. Even when the map is centered over Brazil, it's still super wide. Is Brazil really that wide, or is this just another super-imperfect projection that wildly distorts the real shape of land?