The Twine word count does include code so you should be good to go. If you want to check for sure. Do a play-through of the game and highlight then cut and paste the text from each new page into say Notepad++, then you should be able to see the wordcount on the Summary page.
Also keep in mind that any repeated phrases like room descriptions or link text or page headings only count once. So if you use the same link text several times, it only counts once toward the total.
I wouldn't stress too hard about it at this stage, if you win we'll be editing prior to publishing anyway.