That site has been under construction for years but shows a link to another website and contact details.
You say "shows a link"... that means this isn't a redirect but a live website that displays a link to the parent domain. Thus, it is being treated as a live site. The fact that you mentioned it shows up on inside Google's 3-pack results means that it has a verified Google listing.
Based on the limited information you have shown, here are my conclusions:
1. The verified Google listing has consistent citations for the business. Despite having a different parent domain and perhaps similar business license to it, it is still being treated by Google as an independent entity.
2. It has good on-page and off-page SEO.
3. Competition isn't doing things correctly (see 1 and 2) hence why it can rise to the top.
Thus, to beat him, you simply have to execute the basics in local SEO: good on-page (META data, schema, correct keyword diversity, etc.), good off-page (links from related domains AND links from sites which are based in the same city) and have consistent business citations on major platforms.
Another key here is to stop thinking there is a "trick". Treat his site as its own domain, not as a subsidiary of the parent domain and only then you will do SEO with guns blazing.
Have fun.
Source: 5+ years of doing local SEO on dozens of niches plus helped built local businesses do exactly this (build locations on dozens of other cities without having a physical location).
