At the time of the experiment, Illumina equipment was cheaper per base pair and dominates the human genome sequencing market, but it required a much higher initial investment for the equipment (TODO how much).
The reusable Nanopore device costs just about 500 dollars, and about 500 dollars (50 unit volume) for the single usage flow cell which can decode up to 30 billion base pairs, which is about 10 human genomes 1x! Note that 1x is basically useless for one of the most important of all applications of sequencing: detection of single-nucleotide polymorphisms, since the error rate would be too high to base clinical decisions on.
Compare that to Illumina which is currently doing about an 1000 dollar human genome at 30x, and a bit less errors per base pair (TODO how much).
Other advantages of the MinION over Illumina which didn't really matter to this particular experiment are: