Usually, a package comes with binaries pre-compiled for Windows. Thus, all you have to do is extract the package that Nu Replayer and its assets were in, and you are all set. Nu Replayer has been tested on Windows XP through 11. It has been compiled using FreeBASIC 1.09.0.
To build new Windows binaries isn't that difficult, but you'll need to install additional libraries to ensure proper linking. Afterwards, just type in fbc NuReplay.bas NuReplay.rc -s gui in a command shell, or use an IDE able to pass that command.
Regardless of platform, you will likely need to install additional libraries, notably runtime and/or development variants of SDL, SDL_mixer, SDL_net, zlib, and libzip.
Installing under GNU/Linux, on the other hand, is not so simple. Since the architecture for this system is all over the place, no binaries are provided for GNU/Linux, so you must compile from the included source. Furthermore, FreeBASIC has not been seen in any package manager, so you will likely need to download it directly from the developer website and follow its installation instructions. A simple makefile is supplied.
FreeBSD support was added in FreeBASIC 1.09.0. We presume instructions are similiar to GNU/Linux, but this is untested. Feel free to experiment as need be, until you are able to build your own program.
Alternatively, if you can figure out how to use Wine, then you can use it to run the pre-compiled Windows binaries. This is likely the only way to run Nu Replayer outside of the systems above, as FreeBASIC compiler tools are not provided for any other platforms (except DOS).
That being said, it might be remotely possible to compile a native DOS build, but this is extremely tricky to pull off, and is impossible to cross-compile from a 64-bit Windows system. Nu Replayer also does not currently comply with the 8.3 filename system. To summarize, building for DOS is untested.