An important factor is that computing inherently has a numbers of layers of abstraction and function between the end user and the actual functionality. To some extent this is a from of automation in that regularly used actions are packaged into a single simple set of commands.
There is also the fact that more computing power allows more visually orientated interfaces which, can to a degree hide what is going on not to far under the surface. Equally most people experience computing via software, which to a large extent represents picking form a menu of pre-defined options created by somebody else, even when it doesn't necessarily feel like it.
There are analogies to this in other forms of engineering. A trivial example is standardisation of something like screw threads. It is rare that anyone would now bother to design a thread from scratch, most of the time you are picking form a list of available options and the same goes for things like bearings, gears and motors.
There are also ways in which the same advances you are talking about in computing have had a direct effect on mechanical and manufacturing engineering. An obvious example is the proliferation of CAD/CAM software. You can now design a part on a computer, send the file to a manufacturer and have it delivered shortly afterwards and (at least in theory) it could be more or less untouched by human hands in between.
This process cuts out what would otherwise be a huge amount of labour in terms of producing accurate, dimensioned drawings again it is more a case of automating and streamlining a previously existing process than anything entirely radical. But it does strip away one layer of specialist skill/knowledge.
Where it does become more radical is when you st art to integrate physical modelling with automated drafting so you can test and optimise parts and assemblies in a way which isn't really possible with physical prototypes, especially when dealing with cost-prohibitive manufacturing processes.
