I guess on Linux it is more standard to use dynamic linking (as it is easy to install dependencies) instead of static. On Windows everything is statically linked as we don't want force people to include some .dll's with the game. On Linux I don't know what the best way would be in this case. Maybe two profiles in ENIGMA - one statically link and the other dynamically. If you don't use Audio, then only these should be required:
zlib1g-dev libglu1-mesa-dev
But of course without the "-dev", as it is required for compiling with ENIGMA, not running.
For the ones you posted:
g++ - Compiler - used by ENIGMA to make your game. But not required to run it.
zlib1g-dev - Used in ENIGMA engine to pack resources with zip compression.
libglu1-mesa-dev - OpenGL support what is used by ENIGMA for graphics.
libalure-dev libvorbisfile3 libvorbis-dev libdumb1-dev - All of these are for sound. OpenAL (ALURE) is the sound system used by ENIGMA. Vorbis and Dumb just give additional file formats OpenAL can playback.