The syntax shows a "$" as part of the expected variable name, but your example is missing it. Have you tried:
Else I think filemaker is breaking because it doesn't know what to do with a key of "myVariable" for it's key/value process.
It looks like you are missing the dollar sign for the variable name. There is one "param" and that is explicitly the script parameter, otherwise, you can pass in multiple other variables such as $myVariable=test from your example. In that case, you would want to display that variable in your custom dialog instead of the script parameter.
That was the problem. I was just assuming that FileMaker wouldn't make you pass the '$' into the actual URL but I guess I was wrong. I could have sworn that I tried passing the '$' but that fixed the issue.
It might be worth noting that the syntax for the Web Direct URL is the same after the ? char.
Therefore I would expect many of the rules here...
It does not seem possible to pass $$vars...but you can pass $vars to a script that sets them from $vars to $$vars