Try calling wikipediaLink using the $transclude widget with variables as parameters, but surround the variable references / procedure calls in the $transclude widget with "quotation marks", like this:

\procedure wikipediaLink(articleName, linkText:"Wikipedia Link")
  <a href=`https://en.wikipedia.org/wiki/$(articleName)$`>
  <<linkText>></a>
\end

<$let
  article="Aardvark"
  description="An animal"
>

* <$transclude $variable="wikipediaLink" articleName="<<article>>" linkText="<<description>>" />

</$let>

What's wrong with the output now? Why do you think this happened? And is there something that's unexpectedly right?