The Line between where a CPU/DSP, and FPGA and ASIC make sence is dynamic and changes from generation to generation. Multi-Core CPU/DSP's have definitly taken over some but not all the needs of the FPGA, just like today's FPGA's have taken over most of previous generations ASICs, where the ASIC was primarily required strictly for clock speed or number of resources, not volumn.
My FPGA designs today seem to be split primarily into three camps. ASIC Development, Multi-Channel DSP Functionality, Video Functionality.
For those that are planning on developing multi-million dollar ASIC's the FPGA is a stepping stone to prove out and test the ASIC design.
For those looking to run many parallel DSP paths, the FPGA provides more raw crunching than all the single chip DSP's. Even those with 8+ cores. (However the 8+ core chips are extremly capable)
For those working on video path manipulation (especially 1080p and 4k) it is down to just raw optimized throughput of the data movement from function to function. Many of these tasks can be handled by high end GPU's but the form factors of those GPU's don't necessarily fit the requirements of the design.
For every design there is a balance. Many times there's also a mix of components that optimizes that balance.
Pete