Display output is definitely a problem that modern hobby computer and gaming projects run into. And a FPGA is one solution. The Gameduino takes this approach.

There are downsides to the FPGA approach though. Even the cheapest FPGA can easily end up being more expensive (and more powerful) than the system CPU, putting you in a tail-wagging-the-dog scenario. And if you want your project to have a reasonable lifespan, continued FPGA availability can be a problem.

Many projects just drive video directly from the CPU, but that works better when you have something more powerful than the ESP8266 used here. It would be really nice if there was a simple display chip that this sort of project could take advantage of, but I don't know if FPGAs are the answer.