For Dave it's pretty easy, so long as he's acting on his own and not as someone elses agent. Even though he has a global audience, he only has a small physical presence in one place. So for the most part he only has to worry about contest laws that are local to him, even if the winner lives elsewhere. The worst other jurisdictions can do is confiscate the prize, if they choose to spend the effort to intercept it. That rarely happens, although there could be tax/custom charges for the recipient.
For international corporations it's another matter. They have physical offices around the world, which means they need to respect all the contest laws for most of the countries/jurisdictions they offer the promotion in. For instance in the USA, while there are federal laws, there are also 50 states each with their take on exactly what is an illegal consideration or promotion.
Note I'm using "contest" generically to cover all the things giveaways get classified as, be it sweepstakes or gambling. This whole subject is pretty well covered by internet articles....just start searching.