Didn't receive a game

After seven days mark it as not received. I'm not entirely sure as it hasn't happened to me yet, but I think you can still mark it as received if you get the key later (at least for another week I think).

I would try to send him an e-mail and wait for another couple of days, if he is not replying mark as not received. Is he online on steam?

Basically it's your choice. There is no downside in leaving giveaway feedback pending indefinitely.
You may not be able to enter more giveaways for the game in question in the meantime. Not entirely sure about that.

Or you can mark the giveaway Not received. Even then the creator can still give you the game later and you change feedback but if more than 1 month has passed you'll need assistance from Support to change feedback.

If there were several giveaways made, it is quite possible that yours was simply overlooked.

Are you able to leave a comment on the gifter's Steam profile, or perhaps on a screenshot or artwork or something? If so, let them know that is has been a week since their giveaway ended and ask for them to resolve it. Otherwise you'll have to mark it as not-received.

First of all, mark "☑not received".

You may want to leave a comment on the GA you won.
You may also want to note that you have not received any response to your friend request on Steam.
(Screenshots)
You can then talk to Support about the lack of response.

If the sender is not a bot and can communicate with Support, they will be able to find out what is going on.
If the sender is unresponsive to Support's communication, the sender may be judged to have given a false gift.
If you receive a gift that arrives late, change the mark. "☑ received"

In any case, I think that's the story.

If he's offline at steamgifts there probably is a reason, like can't authenticate via browser but still can use the steam client (which maybe just autostarts) or totally different things that explain the absence here. The user doesn't know why you try to add him/her - maybe isn't even aware of it.

As the others stated mark it as not received or keep it clean to "remind yourself".

From time to check back. Be patient :)

One thing that indicates and overlook is that your red +1 mark is blinking. Then the user pressed sent but forgot to add the key.

I had a case where a giveaway creator were offline in steamgifts for 6 months. I left a comment and marked as not received after a week. After 6 months he apologized, provided me a key and I changed the feedback from not received to received.