This was even more important at a time when Microsoft had actual competition in the OS space and people weren't able to just go online and download updates.
Yeah, right. No bribes, no preinstalled software...
They dominated by ... accident.
But the important thing is that the clients pretty much never asked for other OSes because all of their software worked on MSDOS - and later Windows. People bought computers to run their software, so if the software they wanted to run needed MSDOS or Windows, they'd buy the machines that ran that OS.
And by extension, if the software they wanted to run wouldn't run on the next version of MSDOS or Windows, they wouldn't have a reason to upgrade MSDOS or Windows. But from a user's perspective MSDOS/Windows was the best choice because everything supported it.
Microsoft didn't rely on just backwards compatibility (especially since the idea of "backwards compatibility" relies on something to be compatible with in the first place) but it was an incredibly important aspect of their strategy.