The Illumina HumanOmni1-Quad beadchip is a microarray device consisting of 1,140,419 markers which have derived from the 1,000 genomes project. The markers chosen are is high-value regions of the genome: ABO blood typing SNPs, cSNPs, disease-associated SNPs, eSNPs, SNPs in mRNA splice sites, ADME genes, AIMs, HLA complexes, indels, introns, MHC regions, miRNA binding sites, mitochondrial DNA, PAR, promoter regions, and Y-chromosome.
The markers come together to form a sort of individual fingerprint. Germline SNPs are heritable and so can be traced up the line. Some SNPs are more prominent in subpopulations, something that Ancestry.com and other similar services leverage to predict ethnicity.
This paper utilized genomic DNA extracted from the Singapore BioBank. BioBanks tend to record age, lifestyle, family history, and health information alongside the genomic DNA. I (conservatively) assume that the Singapore BioBank at least has familial relations and gender information tied to the DNA. My interpretation is that the ivestigators SNP genotyped using the Illumina Beadchip the genomic DNA from the bank and compared their results with the "ground truth" provided by the genetic bank.
Illumina brochure for the HumanOmni1-Quad beadchip.