The "Flight Tracker" indeed shows the takeoff and landing times. Note that the takeoff times are usually accurate, but the landing times are estimated and can be quite a bit off, especially if the flight does a downwind leg prior to landing. Once, my friend was flying into OAK and they diverted to SJC due to poor visibility on final approach. "Flight tracker" listed the flight as having landed in OAK!

As far as Alaska's "flight status" is concerned, it shows the departure and arrival times according to when the plane pulls away from the gate and when it arrives at the gate. These times should be accurate to within a few minutes, although sometimes a plane can sit at the gate for quite a while after it has "departed" if the airport is experiencing delays/congestion. To the airline, departure time is when the flight "closes" (when it is ready to push). Also, I've noticed at SEA that the arrival time tends to correspond with when the main cabin door is opened and passengers start to disembark.