IntroComp is an interactive fiction competition that was conceived by Neil deMause. Entrants submit excerpts of unfinished games, which the public votes on. Currently, only the top three games in the voting receive placements and are called the ‘winners’. Winners have a year to complete their games before they can claim their prizes.
(reference: IFwiki)
As you can see, it’s not just an intro you’re entering. For it to be a valid entry, you also need to complete the game within the year. So if you entered it into both, you’re legitimately entering a completed game into two competitions simultaneously.