Algebraic notation with RegEx
The use of regular expressions is an implementation detail.

I think you should continue to structure your API as functions that take a higher level input, such as a game text, and destructure it into the end product that your API's clients want.

That said, you can define a private helper that takes a regular expression and does the work of matching the text and extracting group 0.  Then each of your public functions would delegate most of the work to that just providing it with the appropriate regular expression and maybe the index of the group to return.

private function gameTextExtractor(gameText:String, regex:EReg):String
{
    regex.match(gameText);
    return regex.matched(0);
}