What you linked to is “nothing old.” See https://en.wikipedia.org/wiki/Rail_car_mover – these things are still made and are in service today.
On the other hand, I’d never seen that particular model of Evans Auto-Railer before. There’s quite a bit of technical material surviving on them, and how they differed from most other types of ‘hy-rail’ vehicle.
Note in particular the extreme lightness and relatively long travel of the rail gear. These were designed to be fully-capable road vehicles, not just the compromise that most existing car movers (including most of the pickups modified with hydraulic lifts fore and aft and special wheels with greater offset to give standard-gauge track) are.