Is the technology "identitas v1 forensics chip" related to microarray technology?
Interesting question. The answer lies encoded in our DNA. If you take eye color for example, the genes important here are well known. The most important are OCA2, HERC2, SLC24A4 and TYR.

These are involved in different parts of the pigmentation process, any mutations in these genes lead to changes in pigmentation. Since also the variants, which lead to a altered pigmentation are known, you only need to analyze some cells containing genomic DNA from your suspect to check for these mutations (or SNP, single nucleotide polymorphisms).

The same is true for hair and skin color. So if you identify one or several mutations in the MC1R gene, you can be pretty sure, that your suspect is red haired, has pretty light skin and a high chance for green eyes. 

This technique doesn't need to know the exact expression of a certain gene, but needs information on the cause for a phenotype (like skin, hair or eye color) and the causative gene.

The "Identitas v1 forensics chip" is a microarray chip, unfortunately, the company website is not really a source for information. You can find some in the New Scientist article you linked. This is basically a microarray (or chip) where all the forensically interesting and known SNPs about how a person looks like are analyzed.
It gives basic information (or at least a chance) how a persons looks like, what CSI does in the series is usually widely exagerated.