Quebec has more stringent sweepstakes laws than the rest of Canada:
Companies don't exclude residents of Quebec from sweepstakes because they don't want to advertise in Quebec, or because they have anything against the residents of that province. The reason why so many sweepstakes are void in Quebec is that the sponsors must follow a stringent set of laws set out by Quebec's Regie des alcools, des courses et des jeux (RACJ), which governs alcohol, lotteries, contests, gambling, and more. ...
For example, in order for sweepstakes with prizes worth more than a certain value to be open to residents of Quebec, the companies sponsoring the sweepstakes must take some or all of the following steps:
- Register the sweepstakes rules and all advertisements used to promote the contest with the Quebec government at least 30 days ahead of the sweepstakes' launch.
- Publish the full text of the sweepstakes' rules at least 10 days before the giveaway begins.
- Pay a fee of up to 10% of the sweepstakes' value, depending on who is allowed to enter.
- Agree to allow the government of Quebec to mediate any lawsuits arising from the contest.
- Follow strict guidelines about the contents of the sweepstakes rules.
- Allow the government of Quebec the right to approve any changes to the giveaway that need to be made once it has started, and to approve canceling the giveaway if it becomes necessary to do so.
- File a written report after the contest has concluded, attesting that the prizes have been delivered or attempted to be delivered.
- Agree to let the RACJ mediate any disagreements with the public.
- File security in the amount of the prize value, to ensure that the prizes are actually awarded.
The full set of laws can be found in chapter L-6, r. 6 of Quebec Consolidated Statutes. Note that under Quebec law, a "publicity contest" (concours publicitaire) is
a contest, a lottery scheme, a game, a plan or an operation which results in the awarding of a prize, carried on for the object of promoting the commercial interests of the person for whom it is carried on.
So even though chance plays a minimal role in the contest you've described, it's still regulated by the stringent requirements of Quebec law.
In contrast, in the rest of Canada, promotional contests are governed by Section 74.06 of the (federal) Competition Act. A set of enforcement guidelines can be found on the Competition Bureau's website; they basically require anyone running a contest to:
give "adequate and fair disclosure... of the number and approximate value of the prizes, of the area or areas to which they relate and of any fact within the knowledge of the person that affects materially the chances of winning;"
not "unduly delay" the distribution of the prizes, and
select winners on the basis of skill or on the basis of random chance. [I think this basically bars giving the prize to the boss's nephew.]
However, there is nothing about fees, securities, publishing the rules in advance, submitting one's advertising materials to the government, etc. Given the relative ease of running a contest in the rest of Canada compared to Quebec, one can easily see how a company might not find it worthwhile to allow Quebecers to enter and win.