Z-DOS was a version of Microsoft

Microsoft

Microsoft Corporation is an American public multinational corporation headquartered in Redmond, Washington, USA that develops, manufactures, licenses, and supports a wide range of products and services predominantly related to computing through its various product divisions...

s generic MS-DOS

MS-DOS

MS-DOS is an operating system for x86-based personal computers. It was the most commonly used member of the DOS family of operating systems, and was the main operating system for IBM PC compatible personal computers during the 1980s to the mid 1990s, until it was gradually superseded by operating...

 specifically written to run on the hardware of the Zenith Z-100 personal computer

Z-100 (computer)

The Z-100 computer was an early microcomputer made by Zenith Data Systems . It was a pre-assembled version of the Heathkit H-100, which left the final component assembly to early computer hobbyists.Z-100 Computers were early personal computer era alternatives to the hardware system that won the...

.

The Z-100 used a 8086-family microprocessor, (the Intel 8088

Intel 8088

The Intel 8088 microprocessor was a variant of the Intel 8086 and was introduced on July 1, 1979. It had an 8-bit external data bus instead of the 16-bit bus of the 8086. The 16-bit registers and the one megabyte address range were unchanged, however...

) but otherwise had a completely different internal architecture than the IBM PC.

At the time Microsofts MS-DOS wasn't specifically geared to any specific hardware platform, it could run on any system as long as it used a (16-bit) 8086 or similar microprocessor.
A situation completly like the popular CP/M

CP/M

CP/M was a mass-market operating system created for Intel 8080/85 based microcomputers by Gary Kildall of Digital Research, Inc...

 systems of the time, which used an (8-bit) 8080

Intel 8080

The Intel 8080 was the second 8-bit microprocessor designed and manufactured by Intel and was released in April 1974. It was an extended and enhanced variant of the earlier 8008 design, although without binary compatibility...

-family (8080, 8085 and Z80 among others) microprocessor.
Just like CP/M this early form of MS-DOS relied on a, (CP/M like) platform specific BIOS

BIOS

In IBM PC compatible computers, the basic input/output system , also known as the System BIOS or ROM BIOS , is a de facto standard defining a firmware interface....

, for hardware independency. There were dozens of such versions, each geared to a specific computer.

Only later the "MS-DOS" that we all know, became the rebranded version of the IBM specific version of MS-DOS, (known as PC-DOS

PC-DOS

IBM PC DOS is a DOS system for the IBM Personal Computer and compatibles, manufactured and sold by IBM from the 1980s to the 2000s....

) which (as "MS-DOS"), was sold to IBM PC (clone) makers.