I always kind of looked at him as a big white robot thingy with a living cat thingy on top.

Alternatively, he could have been a real thingamajig with Reeves controlling him by means of 'sending orders'. In the advanced world they lived in, it's possible that Cait Sith was partially alive, or even that Reeves was able to 'feel' what his robot was feeling via some kind of magic and/or technology.