You need to go the other way in this situation; the moose is traveling toward the opposing lane, and steering that direction still puts the vehicle on a collision course with it. Steer toward the direction the animal is coming from (like I had to outside Great Falls this summer, when a deer jumped in front of the Prius), not the direction it's traveling, and you may be able to get the clearance to avoid hitting it. Of course, for the Jeep driver in question--it's broad daylight, you can see the moose(s), and there are a bunch of stopped cars on the road. Anyone who isn't an idiot would have slowed down already and proceeded with caution.
^^^ This. Pay attention, anticipate dangerous situations and drive defensively. Sadly, this is completely lost on the majority of drivers.
What you suggest is often the policy used by air traffic controllers to vector aircraft away from a potential conflict, i.e. steer towards where the 'target' was rather than where is going to be..
I was going to comment similarly to the above re the Jeep driver, but I can't say the driver could have seen the moose (it isn't clear, the camera is on the side of the road), and anyway, he has a right to text/play games/adjust whatever while driving! The young moose should have known! He was lucky it was a young moose, not a full grown one. I wonder if the moose survived without serious injury?
It seems likely that the closer moose could have been hidden behind the roadside vegetation until 1 or 2 seconds before impact. But the second moose in the field, and the many looky-lou's on the roadside, should have been clues, visible and raising alerts long before. Between text messages and games. Despite seeing it get up and run off after impact, I'd have a hard time believing it did not sustain serious injury.
Open the YOUTUBE and there's a description of the scene - including that the driver didn't seem aware of the need to slow down when there is a flock of cars parked watching wildlife. It also said "The moose left a skid mark of hair on the road and limped off slowly into the bushes. Parks and Rec said they followed the moose tracks a ways and it seemed to have walked off, so it might have made it!"
DON'T do that in a Canadian national park, such as Jasper! You could be charged with endangering wildlife. It's certainly "driving with undue care and attention" at the very least, not slowing because there is "something" going on on the side(s) of the road. The alternate view is slowing endangers traffic, but the reality is you MUST be ready to stop at any time on any road. It's actually legal (in Alberta anyway) to stop in a "travel lane" to let out a passenger, or pick up one. So "be careful out there" and drive safely!
And even in other places where in-lane passenger stops are not permitted, there are still plenty of reasons why vehicles ahead may need to suddenly stop to avoid various road hazards -- not just animal (wild, domestic, or human), but also vegetable (e.g. falling trees, power poles) and mineral (e.g. boulders, sinkholes, collapsed bridges).