It seems a more important distinction than basing it on the addressing. Unix has been 64-bit AFAIK since the days of the greenscreens, while Microsoft kept escalating the bit number as time went by. The addressing is just a non-paramount choice, while the bit number on the colors used by the graphics system is actually visibly distinguishable and grew over the years along with the technology.
There big difference between 16 and 32 bit, first of all this is not address space but size of registers. Why this importation? This is because how fast processor can calculate big numbers, If we assume that we have multiple processors that have same speed but different registers then then in same time:
8bit will calculate values up to 255
16bit will calculate values up to 64Ki (64*1024^1)
32bit will calculate values up to 4Gi (4*1024^3)
64bit will calculate values up to 16Ei (16*1024^6)
And current processors aren't in reality 64bit but 256bit but because nobody use 16Ei values it calculate smaller but multiple values at once (SEE, AVX-512).
Address space grow too, but sometimes it can be bigger or smaller than processor. Some 8bit processors can have 16bit address space and today 64bit processor have only around 48bit address space (
https://superuser.com/a/168121/368048)
And why its matter? It determine how big and complex game can be. Of corse in today times 90% memory is used by graphic stuff but still sometimes today games can crate things that was impossible for previous generations.
Btw UNIX on what machine? First of all Microsoft is not responsible for change of bit numbers but Intel or AMD. Second we are discussing home computers not super computers (that many times uses UNIXs).