The above poster is mistaking the "rule" that only the Mercator projection allows for straight lines to represent the meridians and parallels of the map. While this is true for both longitude and latitude on Mercator, only longitudes are allowed to be straight on pseudocylindrical projections (like the one shown in the OP). Since the map in the OP only draws along horizontal lines it's fine to use that type of projection.
Cylindrical (Mercator): https://en.wikipedia.org/wiki/File:Mercator_projection_SW.jp...
Pseudocylindrical (Wagner): https://en.wikipedia.org/wiki/File:Wagner_VI_projection_SW.j...