Why might an airline choose to have one of its airplanes do such a thing?
There's a number of reasons why a flight might fly a different route, with Weather on-route being the most common.
However for this specific flight, there's probably a far less common reason - Solar Flares!
You may recall that around the 2nd of April this year there were a number of major solar flares, which have the potential to impact a number of aspects of flight, including communications. As the impact of the flares is greater around the poles, for the few days following a large number of flights took more southerly routes, and a few flights that rely on taking a very northerly route were actually canceled as a result.
The more direct route results in using more fuel, but presuming that they had planned for that route they would have taken on extra fuel, and thus other than the potential for the flight time being increased there's no real impact due to the different route.
You can view the first part of the flight path this flight took, along with the full flight plan on FlightAware (Currently viewable without a FlightAware account, but by the time you view it you might need a free account if it's more than 2 weeks old)
Wikipedia has a thought on why this might occur:
Over longer distances and/or at higher latitudes the great circle route is significantly shorter than the rhumb line between the same two points. However the inconvenience of having to continuously change bearings while travelling a great circle route makes rhumb line navigation appealing in certain instances
Of course, with computer controlled flight, any such inconvenience vanishes.
So then we move to the Airlines.net forums:
Several years ago it was quite common for us to be offered a vector 3/4 of the way across the country during the climb out of the departure airport. Eventually flight ops sent out a memo telling us not to accept those clearances anymore because they were rhumb-line direct and actually were longer than the filed route.
However they then go on to say:
Of course current winds aloft must be considered and it does not take much wind to wipe out the difference between great circle and some other logical routing.
So possibly due to prevailing winds, it made less sense to use a great circle line, and to use another nearly-as-convenient method of plotting course, and in this case went for a rhumb-line track?
Naturally without actually asking the airline, we'll never know in your flight's case, but these are some of the possible reasons.
Either that, or perhaps the pilot wanted to test it for a software reason. Or possibly they knew the software was having problems with great circle paths. I can think of a few other 'pettier' reasons, but again, we'd just be guessing.