I decided to take a look around on the Air Canada website to see what kind of flights are available from Whitehorse (never know if I'd like to go there one day!).There are only two flights a day that go from Whitehorse to Vancouver - 7:00 am (so they'd have missed that one since they got to the airport at 9-ish as you saw on TV) and 13:45.
The 13:45 flight to Vancouver arrives at 16:13 and there are several flights that goes to Edmonton (17:05, 20:10, 21:20 and 23:10), all have the next flight to Regina leaving at 06:00 and arriving at 07:36 as we saw. The Vancouver to Calgary flight would arrive more or less in the same time-frame as the Edmonton one, but there'd be plenty of time for Hal/Joanne to get up to Edmonton from Calgary as it's less than three hours from airport to airport (they could even have rented a car and driven up there if they had to!).
Real surprised there isn't a flight that goes directly from Whitehorse to Edmonton or Calgary. There isn't an option to fly to Yellowknife then on to Edmonton, either.
Good question about Greyhound, but since Air Canada is the main sponsor of the race, they probably could only limit themselves to using flights on this race. Too bad, taking the Rocky Mountaineer train would have been quite the visual experience.