A quick 2-minute check shows that yes, indeed the site violates Google guidelines. If you check the backlinks using any number of checkers (Open Site Explorer, Ahrefs, Majestic SEO) you can find a number of over-optimized 'unnatural' backlinks residing on spammy link-exchange pages in clear violation of Google's guidelines. The only reason to place links on these pages would be to try to rise higher in Google's search results.

Yes, it feels unfair when Google drops you in search results, and Google has changed the rules over the years and it's hard to keep up with shifting guidelines.

In truth, the website can recover from this. The same people who placed spammy links on 3rd party sites in order to manipulate rankings are probably savvy enough to mount a clean up effort to get those links removed and/or file a disavow request with Google (which basically tells them to ignore those links)

Ironically, Eric Schmidt once tried to scrub Google of unfavorable search results about himself, and he was told they do not do that for individual results. ;)