Absolute value: sometimes CAS is very clever, sometimes not!

[parisse]

It's not really related to domain. It's just that x!=0 evals, while x>0 stays unevaled. I don't think that modifying x!=0 to x<0 or x>0 is a good idea, because it's more complicated to read. In a program, you can play with the answer of domain (or any expression) by disabling auto-simplification and commands like:
a:=domain(1/x); eval(a,1)[1]; eval(a,1)[2]; eval(a,1)[3];