Was this flight a fuel emergency?
There appears to be no emergency. The flight was diverted at 16:58 EST and landed at Bradley International Airport at 17:03 EST. The same flight on 6th Feb landed at Boston at 16:46 EST. So basically, the flight was in the air only for an extra 15 minutes, compared to the scheduled time.
According to § 121.639 Fuel supply: All domestic operations.:

No person may dispatch or take off an airplane unless it has enough fuel—
(a) To fly to the airport to which it is dispatched;
(b) Thereafter, to fly to and land at the most distant alternate airport (where required) for the airport to which dispatched; and
(c) Thereafter, to fly for 45 minutes at normal cruising fuel consumption

So basically, the pilot diverted because the holding time was another 60 minutes and that would've eaten into fuel reserves.

I think the captain meant that the aircraft had only 10 minutes of fuel till he had to dip into reserves (or fly the alternate- it depends) and diverted because of the 60 minute waiting time. He could've been more clear though.

The pilot would've declared a fuel emergency if there was one. So, I think there was none.

Its quite uncommon for aircraft to land on 10 minutes of reserve fuel, though it has happened. In fact, some aircraft have run out of fuel.

You can find details about the ATC in liveatc's audio archives.