Markdown is merely the lowest common denominator of what is essentially a jungle of weird and wonderful wiki languages. The reason it is so under-specified is that it emerged out of the Ruby community in a time where the whole point of Ruby was that it was a scripting language without a lot of appreciation for things like types or specifications. The first serious attempts to unit test and specify ruby itself actually came out of the JRuby community. Which had an obvious need to cover all the complicated stuff that Ruby did so they could handle all the edge cases in the same way. You see the same with other scripting languages where the obsession with specifying what things like Javascript or Python actually do came later in the life of the languages.
I think the main reason for the popularity of Markdown is that is minimal, forgiving, and uses things that are kind of intuitive for basic formatting. * for bold, - for bullets, etc. Similar compatibility issues between various implementations exist for things like Json, Yaml, HTML, etc. Some of these things even have IETF or W3C specifications nowadays. The specifications usually come after things get popular; rarely before.
Whatever the ruby markdown library did was the specified behavior of Markdown for some time. And then of course it caught on and several alternate implementations emerged for different languages; each with their own features added or interpretations of features. Then Github adopted it, added a few features they needed and then it went mainstream in a big way by virtue of world+dog using Github.
At this point Markdown is collection of features that may or may not work depending on which library and language you use; or even where you use it. The simple stuff works everywhere. But your mileage may vary with some of the more advanced stuff like tables for example. Mostly, the Github dialect seems dominant for the simple reason that that is a popular place to find a lot of markdown content.
The problem with alternatives is that they are comparatively less widely used and therefore a bit more obscure. You need good library support across multiple language ecosystems and a lot of the alternatives simply don't have that or enough of a community of users that care enough to fix that. People have their favorites but they can't seem to agree on a single one. So, Markdown it is for most of us. I'm not even sure that is a bad thing.
I kind of like it, actually. It's good enough for my needs. I use pandoc to convert markdown files to html for my website. It supports enough of the Github dialect that I don't have to obsess over what it supports or doesn't support too much. I'm unlikely to convert my content to another format at this point. I use it without thinking in Github issues, in readme's, etc.