The hosted build is something I have used for debugging the ESP8266 implementation. It tries to use as much as possible of the ESP8266 codebase (including the video driver). It's not really useful unless you are interested in further developing the ESP8266 platform firmware, and I should probably stop building it.
If you want to use something on your PC that works more or less identical to the H3 build, you should look at the nextgen branch and Makefile.sdl. Building this version requires SDL 1.2, and the probability that it also works on whatever system you have depends on how close your system is to Linux. 🙂
I am heavily using this version for debugging and development, but I don't want to spend my time supporting a million platforms, so I am not going to provide builds of it, at least not while there is development to do on the H3 platform.