The New England Patriots are not a "dynasty," according to Bob Ryan, and I agree fully. What we have here is a very good -- even great -- team that's the best in the league during this era. What it is not is a dynasty.
Ryan quotes Webster's:
1 : a succession of rulers of the same line of descent
2 : a powerful group or family that maintains its position for a considerable time
and it's only in that second definition that sports can provide a dynasty. It has to be a generational thing, or you're just talking about a great team. For that reason, I'd consider the 49ers under Walsh and Seifert with Montana and Young almost to be a dynasty, as well as the Redskins under the first reign of Joe Gibbs.
I'm not an expert on the NFL, but when I think of the Troy Aikman Cowboys (yes, under two coaches), I see a team that was able to compete as a unit while young and then lost its way as its young talent got too expensive to hold together. Yes, they kept Aikman, Smith, and Irving, but I assume that as those three commanded higher salaries, Jerry Jones could no longer afford the complimentary pieces that make an NFL championship possible. Why did they lose playoff games in 1996 and then collapse in 1997? The offense went from a top-three offense to one of the worst. And that coincided quite nicely with their big three entering their most expensive years.
The NFL has never had a dynasty. It has had a succession of great teams -- about one per decade during my lifetime. The Steelers in the 70s, the 49ers in the 80s, the Cowboys in the 90s, and now the Patriots. Along the way, there's been some other great franchise -- Redskins, Packers, Broncos ... but no dynasties.
Baseball is different, probably because of the lack of a salary cap. The Atlanta Braves have an indisputable dynasty atop their division ("maintains its position ..."). New pieces have come and gone, but the team keeps winning.