They didn't share any source, no. However, the TITLE directive twenty lines or so down from the top in both XENIX.ASM and XENIX2.ASM explains what this is:
TITLE XENIX - IO system to mimic UNIX
Pre-2.x MS-DOS was somewhere between heavily inspired by CP/M and a complete rip-off of it. But with 2.x they decided to go in a quite different direction, and ...
Using SCO UNIX describes the history of XENIX and SCO UNIX and provides a brief summary of the technical differences.
As Raffzahn explains, SCO UNIX is the successor to XENIX. XENIX is a licensed version of UNIX; it was called XENIX because initially, AT&T didn’t allow its licensees to use the UNIX trademark. This was relaxed in 1989, which allowed SCO ...
The source code files in question appear to have the implementation for the MS-DOS 2.0 'XENIX-style' APIs to open/close/etc. files without a File Control Block used in MS-DOS 1.0 and CP/M.
I strongly suspect the authors used 'XENIX' as a shorthand for 'those new-fangled IO methods'.
Nowadays, of course, everyone uses the 'new-fangled' APIs and the FCB APIs ...
In short: not very.
Older versions of Xenix are based on V7 or System III (which are very similar to each other). They had the bourne shell, and large parts of the standard library were already available, e.g. stdio, malloc, alarm, lseek, getenv, but they were lacking many things you'd take for granted: there was no networking beyond serial ports, no ...
The major relationship between MS-DOS and Xenix is that both were Microsoft products. MS-DOS was originally 86-DOS, from Seattle Computer Products, and was licensed by MS to develop PC-DOS. Xenix was a version of Unix which Microsoft licensed from Bell Labs (which was legally prohibited from selling software to consumers) and re-sold.
What exactly were the technical advantages that made their Unix worth more than Xenix?
For most parts: The Name. Otherwise it's simply the next release of SCO's unixoide OS.
They were only sold in parallel for a short time (ca 1989/90). While the latest Xenix version was based on System V R2.3, SCO Unix started out as System V R3.2. But using the same ...
I found the following in the history section of The MS-DOS Encyclopedia (around "Version 2"). Sorry for the long text but I could not find a good way to trim it without losing relevant details. Emphasis is mine.
In developing the first version, the programmers had had two primary
goals: running translated CP/M-80 software and keeping MS-DOS small.
One other difference: Xenix 2.3.2 did not have a block buffer cache. Every version of SCO Unixs I've used did.
Consequence: On an IBM PS/2 model 80 (?, 20 MHz 386, Micro Channel) the max throughput to the hard drive was 35 KB/s. On an AST Research 486 with a DPT SmartCache SCSI controller (high end for 1992!) we maxed out at 45 KB/s.