Link Age and Domain Age are totally different things.
Domain Age denotes the age from the time when the site was registered (Source: WHOIS information).
Link Age denotes the age from the time the specific page/link was created (Source: Document Inception Date).
So, over time, you can have many new links in an old site.
Domain age has significant influence in Google Rankings and it is proven. Old sites has been awarded with better ranking since 2005, as Google found that spammers evacuate site quite frequently.
But, many Search Engine Optimizers (SEOs) debate over the positive influence of “Link Age” in SEO. Many debate that Google likes fresh contents in old sites. So, for Link Age, this is somewhat inverse relation to positive SEO factors involving age. i.e. the newer the link age, the better the ranking.
Darren McLaughlin, in the Sootle Directory blog, mentioned the Google Patent using Document Inception Date for the freshness of links.
However, there are a great number of SEOs that believe that old links are better than new links. In their view, link age is also important as domain age. Again, it is also evidant that Google punishes the pages that have not been updated for long time. However, in the view of these SEOs, the freshness of content in old link has more marketibility than new links.