To actually answer your question, they probably can sometimes track four dimensional trajectories, however not always, and they are not going to give you that data because that would reveal how good their tracking algorithms and sensors are. Sensor fusion is a thing:
Even with fusion, the fewer the sensors the less accurate the tracking will be. In these videos there may only be one or two sensors actually tracking the object.
Hitting a target with a missile is a somewhat different problem, you just have to get the missile there based on whatever data you have (which might be from the carriers sensor data, the missiles own sensors, or both). For example an IR missile doesn't know the location of its target, it just knows how far off center the IR light from the target is from the missiles current flight path and it can correct course based on that simple angular offset to eventually hit the target (with some additional math since the missile has to go to where the target will be when it gets there.) Similarly stopping an evasive incoming missile does not require that you know its exact location. Also as a defensive missile gets closer to the incoming missile it may be able to get better data on where its target actually is and how it is moving. Missiles move very fast so on the final approach there is not much ability to change direction at all, it would require too many g's to turn the missile, so you can model the final approach as a straight line. When it's close your own tracking systems probably work better as well because the targets cross section takes up more of the sky.
https://en.wikipedia.org/wiki/Sensor_fusion
Even with fusion, the fewer the sensors the less accurate the tracking will be. In these videos there may only be one or two sensors actually tracking the object.
Hitting a target with a missile is a somewhat different problem, you just have to get the missile there based on whatever data you have (which might be from the carriers sensor data, the missiles own sensors, or both). For example an IR missile doesn't know the location of its target, it just knows how far off center the IR light from the target is from the missiles current flight path and it can correct course based on that simple angular offset to eventually hit the target (with some additional math since the missile has to go to where the target will be when it gets there.) Similarly stopping an evasive incoming missile does not require that you know its exact location. Also as a defensive missile gets closer to the incoming missile it may be able to get better data on where its target actually is and how it is moving. Missiles move very fast so on the final approach there is not much ability to change direction at all, it would require too many g's to turn the missile, so you can model the final approach as a straight line. When it's close your own tracking systems probably work better as well because the targets cross section takes up more of the sky.