* Experimental processor design. If you want to make a processor with its own custom instruction set, or modify an existing processor design, you need an FPGA to actually see it in action.
* Synthesizers and audio filters. You can do a lot of low latency signal processing compared to even a beefy microcontroller with an FPGA, so if you want to make your own synth sounds in hardware, an FPGA might make sense.
* Computer vision stuff. If you want to make some gadget that does some kind of image processing that is streaming from a camera, and FPGA would work, especially if you wanted it to be small/portable.
* High bandwidth or low latency SDR applications.
Electronic warfare is most commonly the disabling of enemy radio frequency equipment (radar, communications, targeting, etc).
Given, this is just my opinion on the matter, so take it with a grain of salt.