I can tell you that in pretty much every presentation context a graph (no matter what graph) beats a table. We are much more accustomed to visually processing things than through numbers. I mean take the example of the given map (and let's keep it to the "simple" winner takes all map), the table for this map would definitely be so big that you could not easily tell which party won more counties. With the map it would be one glance.

Yes as the author points out it does not tell you anything about the number of people in the county, but trying to convey information in graphics well is difficult (and when people get it right it can be truly amazing, i.e. take Roslings talks, which really visualised public health effects and enabled many people to understand for the first time). However, everyone who regularly has to present data to people should invest time into learning about how to graph and visualise your data.