Are digital signal processors categorised in ASIPs?
ASIPS are instruction pipelines specifically tailored to a purpose, more along the lines of an FPGA where the algorithm is implemented on a hardware level. The algorithms can still be changed somewhat by loading different instructions. DSP's are not necessarily ASIPS because most DSPs do not have configurable logic. 

An example of this would be intels new xeon chips that integrate re-configurable logic that can be tailored to specific algorithms. 

Personally I think the term ASIP is perfectly useless.