I wonder what the author would think of the Drake Equation or quantum mechanic's superposition, as they seem to check a good deal of these boxes but are widely regarded.
I don’t know what equation you mean by “quantum mechanics’s superposition”, but most equations used in quantum mechanics actually are meaningful and represent some physical phenomenon to a high degree of accuracy though (I.e. they make predictions which can be verified through observation and measurement).
So yes, the Drake Equation is dimensionally sound.
It is also a true equation. Not observed to be true, but reasoned to be true. The right hand side is the left hand side multiplied by some non-zero factors, and divided by the same factors, and rearranged (into the multiplication of a time rate, 5 ratios, and a length of time).
There’s still a lot of uncertainty about the numerical value of some of the factors — but the math is sound.
Therefor I wouldn’t put the Drake Equation in the same category “mathiness” that the original article is talking about.