Yes, OpenCL is an API and shader language for GPGPU usage.
Yes, it is a competitor to CUDA.
No, CUDA is not the majority of GPGPU usage (although in 2012, 3+ years ago, this may have been true depending on who you spoke to), OpenCL now is.
No, CUDA and OpenCL competing is not an issue, as Nvidia is a founding member of Khronos's OpenCL committee, and Nvidia uses a merged compiler backend for all their shaders (including OpenCL and CUDA); neither API will produce better optimized binaries than the other on Nvidia hardware.
Yes, there are OpenCL implementations for CPUs: AMD and Nvidia's implementations both can be executed on x86 CPUs (useful for lock step full program debugging without needing to deal with the async nature of GPUs), Intel has one for x86, IBM has one for PPC/PPC64/Power.
Yes, there are OpenCL implementations for DSPs. That was already a thing in 2012. Sony/IBM has one for Cell SPEs.
Yes, GPUs are in fact highly parallel DSPs.
No, since 2012, Parallela nor P2012 ever took off.
No, OpenCL cannot displace GPGPU because that is like saying Electric will displace the Car. No, instead, we'll make cars that run on electricity instead of gasoline, ie, we'll be changing APIs to more universally supported ones.
Is GPGPU dying? 'Yes.' What is killing it? The march of technology into making EVERYTHING generic processing: floating point used to be a specialized application requiring an optional co-processor: it is now part of the CPU; SIMD used to be part of specialized DSPs, that, too, is now part of the CPU, and that part of the CPU becomes more complex every other generation or so; GPGPUs were merged on-die a few generations back and natively speak to the CPU's memory controller and socket bus as if they were just another core.
And merging GPGPUs on-die isn't even new, if we view them as just specialized highly parallel DSPs: MIPS and ARM SoCs have done this for like the past decade by including communications and audio processing DSPs in the package or on-die.
So, just like the FPU, and SIMD, GPGPUs as highly parallel DSPs are being merged into the CPU.
And, as a side note, you know what this looks like from the other side, a CPU becoming a highly parallel DSP? Intel's Xeon Phi series.
And, as another side note, since it is now a given that CPUs need to be able to do embarrassingly parallel tasks optimizedly, Intel is now tackling the fact that QPI is not scalable across a CCNUMA cluster like AMD's Hypertransport is, and is now moving to embed their Infiniband variant onto CPU and Phi dies, for native 40/100gbit on-die. There are already Xeon E5/E7s slated to have this on a post-LGA-2011-3 socket.
Disclaimer: I wrote DiabloMiner, that popular GPU Bitcoin miner everyone used until ASICs took over.