Is there logic in this sentence? "Authors discovered a gene as one of the genes evolved through natural selection"
Yes, the statement in the news article is not correct; however, it (probably accidentally) isn't quite as nonsensical as it sounds.  

The actual paper that the news article is trying to describe is unsurprisingly more accurate.  


  Here, we found a gene, SLC18A1 (VMAT1: Vesicular monoamine transporter 1), as a positively selected gene in the human lineage. This gene has a human‐unique variant (Thr136Ile; different from other mammals (136Asn)) whose association with several psychotic symptoms has been repeatedly indicated. Moreover, our analysis showed that this variant has been maintained in non‐African populations by balancing selection and had originated around 100,000 years ago, typically regarded as the timing of Out‐of‐Africa migration. 


--Positive and balancing selection on SLC18A1 gene associated with psychiatric disorders and human‐unique personality traits

Here instead of talking about "natural selection", the authors refer to "positive selection" and "balancing selection", two sub-categories of natural selection. Since much of the genome is under negative selection, it's worth noting alleles that are not.


  Didn't all genes evolve through natural selection?


The reason the news article is not nonsensical is that natural selection is not the only force that acts on genomes.  We've known for 50 years that drift is an important factor that influences genetic evolution (wikipedia: Neutral theory of molecular evolution, Nearly neutral theory of molecular evolution).  However, it's pretty clear from the article that the author is unaware of these concepts and probably doesn't understand the significance of the paper.