The syntax of a language is not usually licensed, just the specific implementation of the interpreters and compilers. Programming languages are used to build software like natural languages are used to (let's say) write poems. Specific software implementations could be licensed, like specific poems could be, but the language itself couldn't be.
The particular case of Markdown the language is not licensed. And its reference implementation, Markdown, a Perl script that implements the parser and HTML generator, is licensed with a 3-Clause BSD license.
There was a related question on Software Engineering if you want to read more details:
What constitutes a programming language and how does one copyright a programming language?