This kit seems very similar to the famous Altair computer which spawned MS-BASIC and CP/M. Anything like Unix and C is not desirable on such a system. Even a 'text editor', as we understand them today, is a reach on such machines.
You could build your own world, but you'd probably have to do it writing ASM out by hand and then entering through a cumbersome line editor. For most purposes, that's too hard, so you would probably invent a very 'basic' line-level interpreter. But, given what we know now, you'd probably come up with a better disk operating system.
It's actually pretty surprising how much you can achieve with these 8 bit processors. My favourite example of pushing the 8 bit Arduino processor to the limit is this - 3D rendering at 320x240 x 16 bit: http://hackaday.com/2016/01/02/better-3d-graphics-on-the-ard...
That demo is rather impressive, but the AVR in an Arduino is much faster than a Z80. This machine is running at ~7.37MHz (which is fast compared to old Z80 based personal computers) whereas the Arduino typically runs at 16Mhz. Further, an instruction takes a minimum of 4 cycles on the Z80 and many take longer whereas most AVR instructions take only a single cycle.
You could build your own world, but you'd probably have to do it writing ASM out by hand and then entering through a cumbersome line editor. For most purposes, that's too hard, so you would probably invent a very 'basic' line-level interpreter. But, given what we know now, you'd probably come up with a better disk operating system.