Unless I'm misunderstanding what you mean, this isn't possible in a backwards-compatible manner: It's perfectly reasonable for pre-existing Markdown to have content like "Bob pays $1 for bananas, Susan pays $2," which would mis-render a normal sentence as if it had inline math content.
The blog post author's proposal is the most reasonable one: it's both backwards-compatible (the triple-tick "math" group was not already defined or, if it was, a new unique identifier could be used) and doesn't produce any ambiguities with other parts of the Markdown grammar or non-semantic text. Finally, it avoids parser composition, which is a source of all kinds of nasty differential bugs.