Does the S88 MK3 come include the Machine 3 software?
Quick answer: no.
This is what it includes:
https://www.native-instruments.com/en/products/komplete/keyboards/kontrol-s49-s61-s88/included-software/
Wow, ok. That makes no sense whatsoever. So, I guess it includes only the Maschine 2, as Maschine does.
No it doesn't include any version of Maschine. Did you not follow the link and read the list? Maschine software is bundled with Maschine controllers, as they're designed to be used together.
The MK3 keyboards don't have the same integration with Maschine software as the previous MK2 keyboards, so it does make sense, in at least two ways. Firstly that the software is designed primarily for the pad based controllers, and secondly the full integration with MK3 keyboards was removed.