https://gleam.io/guides/no-purchase-necessary
>A contest is a type of promotion you can run in which an element of skill is involved. For a promotion to be considered a contest, entries must be skill-based and winners must be chosen based on merit. Meaning they cannot be drawn randomly.
>Examples of contests include:
>"Best Photo" Competition
>Voting Contest
>Sports-Based Contest
>Essay Competition
>"Tell us in less than 20 words..." Competition
>When you run a skill-based contest, winners are not randomly drawn, hence removing one of the three defining features of a lottery. As a result, contests are not impeded by No Purchase Necessary laws.
>...entries must be skill-based and winners must be chosen based on merit.
In the scenario above, it takes skill but not the participants' skill, so it is essentially as out of the control of the participants as which number is drawn by a ball machine.
Now, if the skill in question is that of picking a winning sports team, then were talking about gambling which, of course, has its own set of rules and would be a stretch to apply here in any case.
Overall, it seems this contest would be on shaky legal ground one way or another.
That's not a factor WRT the law in question.
The law states that if you take money or some financial consideration for a chance (that is not based on your skill) of receiving something of value, then it is effectively an illegal lottery. It doesn't matter whether everyone wins or loses.
This is usually addressed by allowing people to enter without making a purchase (entry form, postcard, etc). But, here, that obviously would be an insane offer, so doesn't really apply.