Why doesn't the site punish those who take advantage of its system?

Exactly, as it gives you pause...

Oh my, You're totally right.
I apologize I did not see the dot.

Ask support to set the feedback to received.

Edit: Contact the group's owner, to get them kicked from the group.

As I recall, they can't mark the giveaway as not received until 7 days have past. Additionally, within that time they are not allowed to contact you. Only after 7 days they may contact you, though it seems they may not be required to.

I see you left them a message saying they won your giveaway, though you didn't ask if there was anything wrong. They may have already been aware and simply waiting 7 days to provide the feedback. Unsure what was sent in the email, though it may have gone to spam which may be why they never responded there.

It is unlikely they'd be waiting for the exact moment to mark the giveaway as not received, giving you time to make the request before they marked it. I'd be wary of rerolling a giveaway in which the key was seen though.

It appears as though a Junior Moderator had contacted them requesting information hours ago.

In case it was activated on alt, it is better to not delete, so people can see it. Ask steam support for a time when was key activated, if it was after giveaway ended, it is exact proof of alt activation you need. Then post proof in giveaway, so other users can see it.

I had someone recently give me my first Not Received. The user had originally marked it as Received, and I can recall checking their account and seeing it there. A week later, it's suddenly Not Received and the game isn't in their account. I highly suspect it's set private now.

As it was marked Not Received, and I have no proof, support was not able to resolve this situation and I'll now likely have this mark on my account forever.

Now in the steam beta, you can mark individual games as private. It can happen, that they activate the key then mark the game private. You should ask them to put the game on wishlist, you cant put privated games on the wishlist.

Many will not ask a winner, because it is too much hassle. Because of that a private profile can be considered at least a try to abuse the system. As you did not elaborate on what kind of abuse you are talking about, I thought every kind should be mentioned.
If it is an obvious alt account, hope they win one of your giveaways, ask for a re-roll providing proof of it being an alt account (and which is the primary) and support works very fast (in my experience) and permanently suspend the accounts.

A private profile does not break any rule, but looks fishy - imho.
As much as I like privacy in general, I dislike private Steam profiles in connection with Steamgifts. Every time I got a winner with a private profile, I have to find a way to contact them, ask them to set it to public, so I can check for non activations. That has, in some cases, taken a lot of time in the past.

So far they haven't responded and they likely won't.

That is a great suggestion, missed that bit of information so far.

Ah, gotcha. Since the scenario is fairly detailed, I will assume this actually happened.

It is likely the winner has done something with the key, indeed (activated elsewhere, sold it, etc.), and that would be a breaking of the rules ("All keys must be activated in your account")... though undetectable by support (especially if it happens only once). I mean, from support's point-of-view, it is possible (even if not very likely) that the key was invalid from the beginning, and the winner's worst sin would be poor communication...

Either way, it will be this winner's loss -- I am sure he/she will get some blacklists, get kicked from groups... Also, I imagine that if this person does this multiple times, then that "possible" above becomes "nearly impossible" and then support might take action.

Sorry for the bad situation. I myself have a winner who just completed 1 week without giving feedback on my GA, so I might go through a similarly annoying process as you did (or maybe not, wish me luck).

Cheers!