It is not only Quebec but also many States in United States do not allow sweepstakes/contests and lotteries because of the different Laws written for consumer protection or moral purposes under Blue laws".
Blue laws are designed to enforce religious standards in many States and Provinces in the United States and Canada.
That is why some states do not have lotteries, or do not allow gambling. On the other hand, there are restrictions on liquor sale too. Alternatively, do not allow sweepstakes drawings.