As pornel pointed out, CSS Variables are really custom properties that cascade and inherit just like regular properties. Since "$" is used by CSS preprocessors for variables that work in a different way, I think Tab felt that it would cause too much confusion to use the same symbol. The set of remaining ASCII non-alphabetic characters that CSS doesn't use is pretty small too; perhaps "$" is slated for use by some other feature.
There's also a desire in the WG to have a consistent naming scheme for custom CSS things, including custom media queries, custom pseudo-classes to use in selectors, etc. "--" is something that doesn't scream "variables" and so would be usable for those other things.