Note that these companies are not doing DNA microarrays in the sense you're describing (which is for quantifying gene expression by mRNA level). RNA-seq is (now) arguably better for this purpose as well (better dynamic range, primarily), but again this is not what any of the ancestry or personalized genetics companies are doing.

In this case "SNP microarray" is a "digital" (or binary) readout of the genomic DNA sequence; specifically the array has attached to it sequences that match both the "reference allele" (e.g., a "G") and the "alternate allele" (e.g., "A" or some other base). Note that across the world's population, most sites in the human genome are "bi-allelic" meaning that there's really only two variants at each site, though of course it is possible to have tri-allelic or even fully polymorphic (A, T, C, or G) sites. For the purposes of ancestry, bi-allelic identification of commonly polymorphic sites is adequate, though the more sites and the rarer those sites are in world populations, the more specific you can be re: ancestry. This is why the gold standard for ancestry and haplotyping is whole genome sequencing-- you simply get far more informative sites to map to other populations.