I had so many questions about the story! Did the CEO actually use the items or otherwise take them away? Or did he just unwrap them, removing the name tags? Because if the items can be returned intact, it would be very easy to figure out who they were from, and resume the game. Like the General Manager privately asks Bob what he gave, Bob says "a yellow scented candle," the GM pulls that from the pile and gives it back to Bob, who rewraps and relabels it, and secretly gives it to his recipient.
If the items are gone for good, I would feel like someone needs to pay for that, either the CEO or the General Manager. But, it seems like they're both above the workers who were participating, and I can see how if neither offered compensation, a worker wouldn't feel great about pressing the point, especially if the items were small. But ethically I think the General Manager or the CEO is obliged to pay for the items they lost/inadvertently took. The GM was pretty careless with the items left in her safekeeping--she couldn't have put them in a box or bag labeled "Office Secret Santa--see GM"? Yeah, yeah, she thought the CEO wouldn't come back early, but a box/bag would have been such a small extra step that might have made the difference here. And, to me it would be very sensible to corral them all into a container anyway--I would have done it just to make sure I could carry them all and didn't drop any etc..
As for the CEO, there's really not much info about what happened or his reaction. Worst case, greedy spoiled pig who decided to claim any gifts within reach--no sense asking him for compensation, obviously, even if he owed it (should NOT have put gifts anywhere near his stuff, then). On the other hand, gifts left on his desk containing only one name (really the recipient, but he might have thought it was the giver, to him--or not looked closely), around Christmas? Personally I would have stopped to think, "Hmm, this hasn't happened before, I'll just double-check with my GM," but it's not a huge stretch to assume that stuff left on your desk is, in fact, for you. I think it's pretty cheeky that the GM used the CEO's office/desk as storage space, honestly. Best case is the CEO is kind of oblivious but was left really happy that all these workers wanted to get him gifts, even if they are a bit random. He might never have been told, at any point, they weren't for him--of course if he was, he should have immediately known to give them back/compensate for them, but we just don't know.
So basically I think the buck should stop with the GM, who showed poor judgment in storing the gifts and may not have even broken it to the CEO that the gifts weren't actually for him. If she did, and he was like, "Tough taters, finders keepers," that's on the CEO, with the GM still getting secondary blame.
But another thing I'm confused about is that whenever I've heard of Secret Santa games, people usually anonymously give others a small gift every day for, say, a week, then a larger gift at the end when they do the big reveal. From the description of this game, however, it seems like there's just one gift, in which case, I'm not sure why preserving the secrecy was such a big deal anyway--Alice might not know Bob drew her name, but she will find out when Bob gives her the single gift.
Also, maybe if your office can't all be together around Christmas, Secret Santa is just one of those things you should forgo? I'm honestly not sure why people even bother with it, it seems to cause more problems than anything else. I am so not into obligatory gift exchanges, even small ones, as it just leads to people getting more junk they don't need from people who don't know them well. Why not promote the idea of just giving gifts, meaningful ones, to people you are close to and can find something good for? (Away from others, of course, so as not to cause hurt feelings.)