jediviper, are you talking about the original moz domain authority, or are you talking about the new DA 2.0. which was updated in March?
Essentially, the original DA was a flawed metric, a third party tool having nothing to do with how Google actually ranked sites. I'd describe it as a measure of how sites had been built to correlate with outmoded SEO factors (and were no longer in use when DA was launched). DA's main use was by link sellers to increase the value of their inventory.
See this discussion from about six months ago, amd read martinibuster's referenced article in SEJ.... Moz Domain Authority 2.0 Update on 5 Mar 2019 March, 2019 https://www.webmasterworld.com/google/4937759.htm
Apparently, DA 2.0 is designed to track factors that Google actually looks at... and it has some spam detection that might help you evaluate what you're seeing with the two-link blog site.
How is possible?
I can understand how curiosity might make you want to know how they did this, but I wouldn't lose any sleep over it. I doubt that it would be helpful information, since DA is not a Google metric.
Old PageRank could be misrepresented because of the huge latency in Toolbar PageRank. Since TBPR was updated very infrequently, maybe only once every 6-mos or so, the link sellers could rent links to their sites or directories until TBPR kicked way up... then stop renting and be able to misrepresent things for a long while. It was also faked by buying a repurposing old domains, but that has become iffier over time.
You can find techniques for boosting the old DA by searching Google. Most are sleazy at best, and aren't going to help rankings or traffics. Since this is a new blog you're talking about, I'd say that your guess of a redirect is probably a good one.
I cetainly would not encourage your client to continue buying links on basis of the old DA. Best way as far as I'm concerned to improve performance is to look at current competitors and see what they're offering in the way of content and features that users would find useful, and then systematicallly do it better. I would also try to be original, to take new perspectives on old subjects, etc.