The full study is here.

What I read from it, they found a match on the female-line relatives but not on the male-line relatives. These male-line relatives are all descendants of Edward III (via John of Gaunt) just as Richard III was a descendant of Edward III (via Edmund, Duke of York).

The researchers speculate that the match (after statistical adjustment for mutations) on the female line but not on the male line is caused by a "false-paternity event" somewhere along the line. That means that someone's mother was having sex outside of marriage (not that absurd an assumption).

However, the researchers immediately jump to the speculation that "a false-paternity event (or events) at some point(s) in this genealogy could be of key historical significance, particularly if it occurred in the five generations between John of Gaunt (1340–1399) and Richard III" (emphasis mine).

It is speculation that a false paternity event occured, and it could have occured in the generations between John of Gaunt (1340–1399) and Richard III (1452-1485) [5 generations), or it could have occured between John of Gaunt (1340–1399) and Henry Somerset, 5th Duke of Beaufort (1744-1803) [13 generations].

By number of generations alone, a false-paternity event (if it happened) is more likely to have happened in the latter than in the former (which is the bloodline you're asking about). Edit: The researchers say "indicating that a false-paternity event had occurred within the last four generations". That makes the speculation about the very early generations even more just that: pure speculation.

(For completeness sake: another option is that there were multiple false paternity events in several lines after Henry Somerset.) [See reply by /u/fluffyphysics below]

From a somewhat cynical perspective, we found a body in the location where ample historical documentation said it would be. It is always nice to confirm sources but the actual archeological importance is not so great, and vastly outstripped by public interest. It has clearly done great things for public interest in archaeology in Britain which is of greatest importance, but in an academic sense most don't have much to say about it at all.

The cemetery site itself, however, is actually very cool, going at least as far back as late Roman times.

There's an old theory that Edward IV, son of Cecily Neville, was not the son of Richard Plantagenet, and thus had no valid claim to the crown; in which case it theoretically ought to have devolved to George Plantagenet, Duke of Clarence, whose line is still extant in the person of the 15th Earl of Loudoun, an Australian, and thus would have bypassed the Tudors. That theory was popularized by the documentary "Britain's Real Monarch," which would make perhaps for entertaining viewing.