Your reference video didn't help too much ... it is not close up to see working mechanism.
The only one visible motion is Cabin (cable and wheels are not noticeable for their distance from camera or design -flat design). So for the most simple way to animate Cabin keyframe start/end location to get illusion of movement.
For a bit more details you can animate wheels rotation by a driver (instead of keyframe).
Select first wheel and into Y Rotation field type
To animate other wheels right-click on current driver (violet field) and choose Copy as New Driver. Select second wheel and right-click Paste Driver. Select third and fourth wheel and choose Paste Driver too.
If you need to change speed - select the first wheel, click into violet field and change 0.2 to something else. Because other drivers are copy of first one, they stay synced.
To make cabin more natural in motion ... hanging or swinging on cable you would have to use Armature or Rigid Body simulation.
Armature can be animated by Spring Bones addon (that is easier to set, but I got some issues from time to time. Much more stable (but more difficult to setup) is to create "three-edged" object, constraint > Follow Path to cable, simulate movement with Cloth Sim, parent Empties to each vertex and than those Empties use as Target for Bone Constraint > Stretch to ... detailed explanation can be found here
When I saw one of my older post it can be done easier ... Parent Cabin directly to vertices of Cloth Sim object.
- Create this "dummy" object from three triangles.
- Select vertices of top triangle, create a Vertex Group and Assign them.
- Add Cloth sim to this "dummy" and under properties Shape > Pin choose created vertex group.
- Select Cabin than dummy, switch to edit mode, select only three vertices of bottom triangle and Parent Ctrl+P. Do the same for holder part with middle triangle.
- Hanger parent as object to dummy object. Add Constraint > Follow Path to dummy with Target Cable object (be sure origin of those objects is at the same location) and hit Animate path.
(it swings too much, it is for illustration of effect ... if you will animate start slowly it should be fine.)