Did he actually "participate in a contest" though, explicitly? Or was this just a random "I'm giving this away" kinda deal?
See, where you're wrong is Bea can TOTALLY take a week off. Will it upset some people? Sure, maybe. But it's whatever - she's running the contest purely on a volunteer basis.
The dude giving away the NES, to my knowledge, didn't have like a "sign up here specifically to win this prize", it looks to have been an "I am giving this away to a Patreon supporter as a kind gesture" situation. It really boils down to "did he sign up to win a contest, or was the guy just giving away a thing?".
If I make an announcement here on VGS saying that you won a prize, and then I sent out an email to you saying "hey you won a prize" and then you ghost me for a month... yeah it's probably going to someone else. That's... how giveaways usually work. I build contest websites for big companies and there's ALWAYS a rules & regulations page with stipulations like this. If you ghost the giveaway, you're SOL, and rightly so - they can't be expected to sit on your prize indefinitely.